Question about Intel Pentium Gold G5400 BOX

DDR4 Yes. Z270 No. You need a 3xx series motherboard. I would suggest an H310 motherboard since the G5400 is a low-end processor. A B360 is also good, but a bit more expensive. It also depends on the size of the motherboard you need (mATX or ATX). I wouldn't recommend an H370 or Z370 board for the chip, it's a big mismatch in price between the two components that doesn't make much sense.