Not Enough Monkeys

A popular classical problem can be stated as follows:
 
There are five monks, one monkey and pile of coconuts on a desert island. One monk goes to the pile of coconuts, gives one to the monkey, removes a fifth of the remaining coconuts, buries them and goes to sleep.
 
The second monk then wakes up, goes to the pile of coconuts, gives one to the monkey, buries a fifth of what remains and goes to sleep. The other monks do likewise. In due course all five monks wake up and go to the pile of coconuts which they then succeed in sharing equally among them.
 
What is the smallest possible number of coconuts that the pile originally contained?
 
If after the final division there is still one coconut left for the monkey, what is the smallest possible number in the original pile?