Random Numbers Problem

Another problem doing the rounds relates to random numbers. Unlike my previous post, this one might make a (difficult) interview question:

Given a function that generates a integer random number between 1 and 5, write another function that generates an integer random number between 1 and 7.

Obviously you are intended to use the first function for the random element in your solution, not the Random class.

I have been unable to come up with an exact solution that takes finite time for this. I have written some C# code that either gives an exact solution but can theoretically take infinite time, or gives an inexact solution (although to any level of accuracy you like).

You can download my attempted solutions.