Probability is not my strong suite... but here goes...
P(John) = 1/6
P(Henry) = 1/5 (out of 5 after John)
P(John & Henry) = 1/6 x 1/5 = 1/30
Your method is okay, but you need to multiply by two. This is becaue you considered only the case where John is picked first, then Henry. But Henry could be picked first, then John.
So you need 2 ( 1/6 * 1/5) = 1/15