The answer is that security-wise it is a bad idea, but that it is technically possible that it is hashed.
If it is a random subset of your full password you are entering(like first, second, fifth, sixth, and last characters one time, and a different random selection the next time) you could accomplish this by (on initial save)breaking the password into predetermined subsets and then hashing.
Essentially this is just a fancy way to have users enter in multiple passwords without knowing that is what they are doing. The user then knows which password to enter based on which boxes are available.
While there are things you could do to offset it(enforcing much longer initial passwords, strict 3 login attempts/day, increasing the number of multiple-passwords saved and switching to a new one after every login attempt and not allowing repetition until a successful login, etc), this would in general make your passwords shorter(in your case 5 characters) and therefore weaker.
As an aside, the protection you would get from keyloggers in any case would be minimal. It would just require the keylogger to actually look at several of your logins and figure out what your full password is. Better key logging security would be to use two factor authentication, which doesn't have to be complicated or expensive. When the user logs in just present them with a code that they can write down and enter in to login next time.