Regarding 5 minutes - this is fine for fresh Ilford Rapid Fixer. If you are reusing your fixer make sure to do the clearing tests to figure out if/when you need to extend time.
Yes there is such a thing as overfixing. For film you don't have to really worry about an extra minute here and there but if you way overfix, the fixer will begin to bleach the developed silver in the negatives (you'll start to lose density - certainly you do not want this to happen to your shadows).
For papers, it is really best to stick very close to the manufacturer's instructions (again - see Ilford publications) and follow them carefully. Not only do you want to avoid bleaching, but with fiber papers, fixing for longer than the recommended time can leads to longer wash times or other problems. Of course, underfixing is bad for all sorts of reasons.