Its strange, I can't find any reference to a Asus Strix Z270f gaming bios with the number Asus gave you, the earliest BIOS on the Asus web site for motherboard is number 0701. Normally they include them all.
I thought they may have been confused and looked up Z170 but I didn't find 0505 anywhere.
Their web site agrees that you need 0604
but it seems short sighted to release motherboards without right bios on it. The upgrade in store should be free as how are you to know?