[REQUEST] Yahtzee with D20's

I've been trying to figure out the chances of rolling a Yahtzee (5 dice, all the same, 3 rolls) with 20 sided dice instead of the standard 6, but I've been getting nowhere.

Can anyone help?

Rough rules, I roll 5 D20. If all different I just start again straight away. If 2 or more the same then I reroll the rest. No swapping numbers unless I roll a double, then on the 2nd roll all 3 dice show the same (but different to the double) and then I would swap onto the 3 dice for the final roll.

Does that make sense?