gambler,

I think the solution is as follow if you only use 3 and 5 pints vessels:

1) Pour the water half-way on both vessels so that it'll be 1.5 pints of water on 3 pints vessel and 2.5 pints of water on 5 pints vessel.

2) Now, pour the water from 3 pints vessel to 5 pints vessel, so that the 5 pints vessel contains 4 pints of water (1.5+2.5=4).

3) Finally, pour the 3 pints of vessel full. Now, add the amount of water from both vessels (3 pints from 3 pints vessel and 4 pints from 5 pints vessel, which is 7 pints).