Your motherboard seems to only explicitly say that support 1333(OC), 1066, and 800MHz DDR3 ram. However, most "modern" motherboards should be able to, own their own, down-clock your ram to match their supported speeds. A module of 1600MHz ram will simply run at 1333 or 1066, depending on what voltage the bios defaults it at.
If you tried some adata ram and it didn't boot, this could be for multiple reasons.
1) You didn't seat the ram in properly. Simple re-seat it again till it works.
2) It is equal to or larger than 8GB; your motherboard might not support that from a single module (it stated that only a max of 8GB, usually as 2X4GB).
3) You motherboard is old, so your bios might be just as old. The listed support on the site usually holds true assuming it has the latest bios update. It is quite common that older motherboards and bios won't support anything larger than 2GB from a single module. Some are more fortunate, as this might be resolved with a bios update.
4) It just doesn't support it. You can refer to a list of supported ram from ASUS's site down below.
5) Something else, that I possibly missed.
This is the link to the manuals and lists for P5G41T-M LX: https://www.asus.com/us/Motherboards/P5G41TM_LX/HelpDesk_QVL/