Hi Scott and welcome to the forum.
I'd say you have the right amount of nest boxes ... I have two for seven hens and it seems ample. Sometimes they queue up to lay an egg if the box is occupied, sometimes two of them squash in together, but it's never been a problem. They don't all lay at the same time, some are in the morning, some later in the day. I think three boxes between five chickens is more than ample.
Do ask away on the forum if you've any questions. This is a good place to find out more and ask for practical advice!
my chooks: Sage&Onion, Roger the randy cockerel, Squawkbox, Bonnie 'N' Clyde, Pancakes, Custard, Omelette & EggNog. Plus four garden cats and another half dozen feral ones that I feed. And a nursery of pipistrelle bats in the verandah roof ..