probability - When rolling multiple dice, what is the average value if you only keep the highest roll?

These questions come up regarding a RPG in which you roll multiple dice, but only keep the highest value. So, suppose I were to roll 5 dice, each of which has 12 sides (numbered from 1 to 12). If I only keep the highest roll, what would the average end up being?

To throw in an additional level of complication, what would happen if the dice "explode" or "penetrate"?
Explode/Penetrate=If you roll a die and roll the highest value (if you roll an 8 on an eight sided die), re-roll the die and add the results together. Repeat until you do not roll the maximum value.