Since the new update, KSP crash at startup.

some details would be helpful:
Do you have any mods installed?
Have you tried to reinstall the game?

The only thing I can suggest - clean fresh install

First time installed patch -> crash
Then repair files -> crash
Deleted game and folder. Reinstalled game -> crash

If you just delete game folder on Windows machine - there's a folder with configuration settings still in the system.
You can find it somewhere in c:\User\[username]\_(maybe)_Application Data. (Sorry can't say exact location, coz I don't have KSP installed on Windows)
I'm not really sure that folder can cause the problem, but it's safe to delete it in order to reinstall the game.

But for the future, I would suggest you to properly uninstall any software on Windows instead of deleting folders.

check the log file KSP.log in the game folder. It should have some more infos about the crash near the end.

how much RAM do you have ? The most common cause for crashes in KSP is due to Out of memory errors.

This is just a stab in the dark, but are you trying to run 1.5 on a 32 bit OS? The end of 32 bit support was announced on the forums a few days ago, so really old computers won't be able to play it.

Previous versions (with a 32 bit executable) are still available, so if you are running with a 32 bit OS, you may need to revert to 1.4.5. Try that (after uninstalling the old version and making sure the files are gone) and see if it works.

hmm just noticed the last 32 bit install I did download was:
setup_kerbal_space_program_1.4.4.02215_(32bit)_(21664)
That nor any other 32 bits version is at GOG's download page.
So 32 bit version is not available any more (except of course for users that already downloaded.)
The minimum requirements on the store page is 64 bit OS now.
But still ---
Users that still run with (ancient) 32 bit systems and purchased the game earlier on (when 32 bit was supported). And rely on re-download from GOG are in for a BIG surprise if they ever need a reinstall. :-P