Why won’t my brand new ps5 controller turn on

It might be out of charge. If not, it will need fixing (something I'm not good at) and professionals (something that I am not). You could also ask for a refund if you really don't feel like fixing.

I'll at least try: Plug your controller into the console. If it works and charges, then it could be out of charge, or the PS button just doesen't work. You can check that by pressing the PS button while plugged. This might not work if the PS5 requires you to press the PS button to turn on while it is plugged in.

I do not know a lot about it, but someone (not me) might be able to help.