[llimllib]

1) Given a number 1 to 5, get a new one if it's 5, else throw away the MSB, you get 2 bits of randomness per number. Subtract one and call it a.

(Now you have two bits of randomness evenly distributed among the set {00, 01, 10, 11})

2) Get another number 1 to 5, toss it if it's 5, take the LSB. Call it b.

(Now you have another bit of randomness, evenly distributed among {0,1})

3) if b == 1 and a == 11, start over. else return (4b)+a+1

Python implementation (with the -1 then +1 factored out):

  def one_to_seven(debug=False):
    a = one_to_five()
    while a == 5: a = one_to_five()
    b = one_to_five()
    while b == 5: b = one_to_five()
    b = (b % 2) * 4
    if a+b == 8: return one_to_seven()
    return a+b

[llimllib]

patio11's solution is about twice as efficient as mine, and is a much simpler way to think about it.