Most likely I am doing something wrong but all Shamino can seem to do is die. Couple that with the confusing inconsistent way you level up and he is perpetually at lower levels than everyone in my party.
Seriously though can anyone explain the leveling system? Is it really just that British shows up randomly when you are camping? Sometimes I've rested 4-5 times in a row when someone has enough experience to advance and nothing happens.

Yes, the leveling system really is that bad in Ultima 5; you have to rest and hope the RNG decided that Lord British should appear.

There is a way to force a level up, though it comes with the downside of not gaining a stat point. The way it works is as follows:

1. Get your Karma up to 99 by doing good deeds (like donating money to the poor).
2. Let Shamino (or whoever you want to level up) die.
3. Revive Shamino.

If you have 99 Karma, you will not lose experience when you are revived, but your level will still be adjusted based on your new experience total. Unfortunately, doing it this way will deny you the stat bonus. (On the other hand, if you lose a level from being revived with non-perfect Karma), you don't suffer any stat loss, so it is possible, though tedious, to max your stats.)

Ultima 6 got rid of this trick (when you are revived, your level isn't adjusted to max your new XP), but the leveling system is far less annoying and has no RNG component.

It seems to be somewhat random, although I rarely found myself to be that unlucky. (As far as I can recall, there are no time limited quests in Ultima V so there's no penalty for resting over and over as long as you've got enough food, though).

The problem with Shamino is more to do with the general game mechanics of Ultima V, which are rather biased against the Fighter class. Since there are no longer any hard equipment restrictions based on class, Fighters have very little going for them (pretty much just the ability to usually equip a heavier gear loadout, as the only limitation on what a character in V or VI can equip is that the weight total cannot exceed their Strength stat) and the game favours mages very strongly, so poor Shamino just gets left behind (and recruiting any other Fighters is dubious strategy - TBH, it's arguable that having any other party members at all is dubious strategy, as with the ring of invisibility trick a solo Avatar can power through content like a buzz saw, especially if they were imported from Ultima IV and thus begin at level 5 instead of 3).

Have you found the magic axe in Jhelom? That will help Shamino somewhat (particularly with the fact that a ranged weapon is the only way for fighters to really keep up with mages in body count in the long run, and since only the character that delivers killing blows gets any XP ... it isn't till UVII that there is any other way for XP to be gained), but still, the game mechanics just bias against his class, and that's about all there really is to say in the end ...

Actually, not quite true: You start Ultima 5 at 1/10th the XP you had in Ultima 4. If you had less than 1000 XP, you will be level 1. To start at level 5, you need to have had at least 800 XP at the end of Ultima 4. Again, not quite true.

In Ultima 1, rescuing a princess would give you a lot of XP.

In Ultima 4, collecting quest items would give the main character (only) some extra XP. Ultima 4 is also rather biased against the Fighter class. In addition to not being able to use magic, they get no ranged magical weapons. This is particularly bad as only magic weapons will work in the final dungeon. making them incapable of ranged attacks and the second worst class in the game (worst is Shepherd, but that seems to be intentional). Even a Mage is better at ranged attacks late game (not counting spells).

It's really sad that the class system was at its best (and most balanced, for some definition of "balanced") in Ultima 3 and was basically neglected in later games in the series.

Yeah, I was pretty much assuming that if you transfer after completing Ultima IV, you're going to have enough XP to be level 5. You will certainly have enough to be level 4, because IV is one of the four Ultimas that actually has an inherent minimum level requirement on completion, you HAVE TO be level 8 and thus have 6400+ XP. (The others are Ultima I as you need to reach level 8 in addition to Space Ace to get the time machines; Ultima VI as you need to cast a 5th circle spell at one point IIRC so you need to be level 5; and Serpent Isle, where technically there is a level requirement of 4 as Dispel Field - a 5th Circle spell there - is mandatory and you can only cast spells up to 1 circle above your level, although unlike the other three cases in this case finishing the game at at least level 8 is basically unavoidable due to quest XP, indeed in SI I found I would usually finish at level 9 and even about halfway to level 10). Level 5 is very likely, since the snowballing inequality the Ultima IV experience system leads to makes it that much more likely you're going to get the extra 1600 XP needed to reach 8000.

Going into Ultima VI on the other hand you could be lower level, but unlikely to be below level 3 (the game has been finished as low as level 5, meaning you'd go to Ultima VI at level 2, but realistically it is exceedingly difficult to finish the final dungeon below level 7 = 320 transfer XP). Ah, forgot about these. Been aeons since I played UI; and the note about UIV means it's only that much more likely that you won't avoid getting at least 8000 XP before you finish the game :) This is true, although it's mitigated in Ultima IV by a few factors.

- the party class array is not optional, so you can not simply load up on advantaged classes as you could in 5 (where you can quite readily load up on spell casters only, or even just go solo Avatar which has as I've noted some major advantages here).

- melee characters had a good bit more opportunity to have contact with enemies in IV's cramped dungeon rooms. Put Geoffrey and Katrina in 2 and 3 (if they aren't already; they fare best when you recruit them early so they get a lot more XP by dint of having been in a smaller party initially) and they'll have plenty of swings of the Mystic Sword.

- ranged characters were held in check fairly significantly in IV; for one, there were no dropped or found weapons except the melee-only Mystic Sword, all ranged weapons had to be purchased and most were pricey. For two, in Ultima V, ranged equipped characters usually threaten the entire board from the get go (barring LoS blocking obstacles) thanks to Magic Axes; in IV, the fact that you can only attack orthogonally means a lot more enemies survive to the point where the melee battle is joined. Spellcasters are similarly limited for the most part (the Tremor spell is the only player accessible source of damage that can affect enemies not orthogonal to the attacker).

FWIW, in practise, I found that in IV, character level inequality was more strongly tied to how late a given party member joined than to their class. (I also tended to take weaker classes like Katrina earlier, mind you; the fact that all 8 party members need to be alive when you reach the finale strongly incentivises this. Leave Katrina for last, for instance, and indeed you discover some problems with the class balance ...)

You don't have to complete Ultima 4 to transfer to 5. Be aware, however, that if you are not an Avatar, you will be transferred as your current class, and the 5 classes that don't appear otherwise in 5 get no magic.

In Ultima 6, what 5th circle spell do you need? If it's Explosion, you can use a powder keg instead.

Edit: I checked an Ultima 6 speedrun and it seems the player beat the game without leveling up, so at level 3. (3rd level appears to be required because of Dispel Field, but you could get around this by having Iolo cast the spell instead.) Except that:
1. The Bard comes with a Sling. That's one ranged weapon you don't have to purchase.
2. Once you do get Mystic Swords, you can sell them for a ridiculous amount of money (I have a suspicion that this exploit was intentional), enough to get powerful ranged weapons for your party (and more than you can carry); if that's not enough, once all your Mystic Swords are equipped or sold, you can get more.

Actually, at least in the Sega Master System (which, of the two console ports, is more faithful to the original), the requirement is that all 8 characters only need to be in the party; it doesn't matter whether they're alive (though the main character may need to be). (The NES version does its own thing; you don't need any companions to beat the games, and the final dungeon must be played solo.)