How do you fix a 1989 cutlass supreme with a manual transmission that suddenly won't shift into fifth or reverse?

Generally, 5th and reverse are one above the other (same shift fork) so it likely internal trans problem. Sorry Dan the tranny man

Yeah, like Dan said. If you have two gears close to each other go out, you may have had internal damage to the tranny, perhaps a bearing shell out and the pieces either destroying the teeth on those two gears, or just getting it stuck, or both. If you had any weird noises before this happend, its probably your issue. Either way the only real options are tranny rebuild or get a new/different tranny. Replacing it is usually the cheaper option.