After figuring out the Trickiest Pearls problem you've recently found out that over the last few years the performance of the blue and black oysters has greatly improved so that each one of a red oyster or a gold oyster now produce pearls exactly the same with each one of a blue oyster or a black oyster in every aspect except for weight. The pearls produced by the blue oysters weigh 10 grams, black oysters weigh 11 grams, red oysters weigh 12 grams and gold oysters weigh 13 grams, and of course fake pearls weigh 9 grams.

You have 5 bags and each of them either contains all fake pearls, all black oyster pearls, all blue oyster pearls, all red oyster pearls or, gold oyster pearls. You have to find out which bags contain which kinds of pearls in the least amount of weighings possible. Assume every bag contains an infinite amount of pearls.