Not so simple coin experiment

Can someone help me with some reference or any kind of a hint for the problem, which goes like this:

You flip each of *n* coins repeatedly until it shows heads. Let *X* be the number of coins that require at least five flips. Find *P*(*X = 0*) and *E[X].*

I have tried to approach it by employing the geometric distribution for random variables (Olofsson: 118) but I quess this is not the right way to do it, since that could be appropriate if there was only one coin and it would be flipped for X times until the head "occurs".