Here is a tip I heard, and have used:
Store your opened chunks of cheese in aluminum foil. It will stay fresh much longer and not mold!
Julie Notes: Just know that this only works if the cheese is entirely wrapped in foil . . . don't just cap the unwrapped part with foil like I once did. It needs a tight seal to keep air out.
Also, if you're doing this with a big five pound block of cheese, expect to need to replace the foil multiple times before it's used up as the foil get's worn, wrinkled and torn over time. This is probably a more practical method for smaller blocks of cheese. Or, you can cut your large block into smaller blocks first and wrap each individually, to keep from wasting extra foil in the end.