I thought of a better solution, if you know beforehand the weight of a good coin.
Weigh the middle one.
If it is a bad coin, the three bad coins must be in the five coins in the middle. We can weigh just two more coins and find all the bad ones.
If it is a good coin, the bad coins must be in the first five or the last five. And we know how to do that with weighing just two coins.
Bad coins found after weighing just three coins!
But this solution does require that we know how much a good coin weighs.