It does work like that and it is only one weighing.
There is only one bag amongst the 5 bags that contains fake coins.
By taking 1 coin from bag no. 1, and 2 from bag no. 2, and 3 from bag no.3 and so on, then you will then have a total of 15 coins in your hand from all five bags. (nothing weighed yet).
If ALL these 15 coins were real then the total weight should be 15 troy ounces. But at least one of them is fake (if bag no.1) and at most 5 of them are fake (if bag no.5).
Now you place all the coins on the scales in one go. The only possible outcomes are: 14.9, 14.8, 14.7, 14.6 or 14.5 troy ounces, depending on how many fake coins, 1-5, are amongst those 15. If the actual weight is 14.9 then there is only one fake coin, i.e. bag 1. if the actual weight is 14.8 then there are 2 fake coins, i.e. from bag 2.....and so on.
Clever! (congrats to TT!)