for the last two weeks, my computer has been having a weird shutdown process:

When I press the shutdown button in the start menu, everything would close like normally until the screen goes black at the end and then, my components would shut down, but LED lights and fans are still on, spinning. They stay on for about 5 seconds and then the PC would turn back on fully (all components working) and almost immediately turn off again, this time completely.

I am worried that such a double-shutdown process could wear my HDDs as they have to spin up and down twice during the shutdown.

Sometimes, seemingly almost randomly, the PC won't even shutdown - after the components go off, the fans and LEDs would keep working for about 20 seconds and then I hear a BIOS beep and the PC turns on and goes into boot.

This started happening after I installed Windows 10 AND plugged my new internal HDD, so the culprit could be one of them, both or none.

PC works fine besides the shutdown and I don't see any BSODs or such.

My specs:

Intel Core i5-4670
Gigabyte GTX 760 OC
WD Blue 1TB
WD Black 1TB (the new one)
Gigabyte B85M-D3V Motherboard
EVGA 600B-600W PSU