Can you hide during combat or is that supposed to be not allowed in the PHB?
You can hide during combat according D&D5e RAW. But it supposed to cost full action for everyone but rogue, so you wont be able to hide and attack on the same turn in most cases. And unless DM decided to put you against some really stupid and half-blind enemies, you would need to hide in more active way as in "While they blink, I duck under the table and stealthily get out on the left side of it", not just hide in a plain sight.