What (if any problems) will happen if a T8 bulbs are used with T5 ballasts?
It won't work right. It will overdrive the tube (or underdrive the tube) and you'd get short tube life. It may flicker horribly. It may not be able to strike.
Basically the same things that will happen if you put T12 tubes in a T8-ballasted fixture.
It's basically a dumb thing to do.
If you got a wrong thing, take it back and get the right thing.
This may not help, but.. You know, if you have a T8 fixture and it uses anything like standard tombstones (lamp sockets), they sell special extension tombstones to fit a T5 bulb. Or if the fixture already has that upgrade, you can roll it back using standard tombstones.
Though the T5 is slightly more efficient, all things being equal.
T5 lamps are usually 54W while T8 lamps are 32W. The ballast's job is to establish the arc then keep the lamp running at the proper level. T5 lamps are shorter so the initial arc may not work well with a t8 lamp, but the problem will be the T5 ballast will allow too much current to flow and drastically shorten the lamp life, possibly causing the lamp to explode because of high heat. So, no, you should not use the incorrect ballast; they need to be matched to the type of lamp for both the life of the lamp and safety.