Challenge Level

There are 5 yellow balls in bag 1. One ball is transferred to bag 2 which contains an unknown number of green balls.
Bag 2 is then shaken and a ball is selected at random and transferred to bag 1 without seeing its colour.
Bag 1 is then shaken and a ball is selected at random and transferred to bag 2 without seeing its colour.
Finally, a ball is chosen at random from bag 2. |

If I tell you before you carry out this process that there's a $\frac{3}{5}$ chance you will end up with a green ball at the end, can you work out how many green balls are in bag 2 at the start?