Why should you use an annealing temperature about 5°C below the Tm of your primers?
You want to have primers which bind under the conditions of the reaction only to your sequence of interest. If you go too far off the optimal annealing temperature (5°C below the Tm is indeed a relatively good choice in my experience), your will affect the PCR efficency and thus the yield of your reaction.

An annealing temperature, which is much too low allows annealing of your primers to other sites than your intended target with partial annealing or internal base mismatches. This leads to unspecific amplification and lower yields. 

If the annealing temperature is too high no primer binding can happen and you will get not PCR product. Alternatively, partial binding can also lead to misprimed products, although this is much less likely than getting no product at all.