Damsel fish get big. Waaaay to big for a nano, IMHO. And when you include coral and a nem, you're out of swimming room.
Plus, the bioload of a fully grown damsel will mess up your water really fast - corals don't like that, nems just suddenly die, and when they do, they nuke the whole tank.
Best to keep a nano either with only a fish - just one - or corals. I just wouldn't do both. And I'm quite aware they've got pictures on the box - betcha the LFS has a couple on display... They change water daily at the store and rotate the stock in and out; otherwise it'd just be 5 gallons of rotten water on the counter.
I have one in my 5 gallon, and he's been fine for a few months now.
That said, my experience won't always be yours. I got mine when he want a little smaller than a quarter, and he's now a good 1 1/2" long. He'll eventually outgrow this tank, and I'll move him into a 10 gallon (or a 20, if I can at that time). If you're fine with upgrading down the road, go for it, if you're committed to keeping clean water and doing maintenance pretty often.
While I'll have to disagree on the idea that you can only have fish OR corals in a pico tank, I will say that it does make everything a bit harder and things can go down the drain pretty quickly. With light feedings every 2 days, I get up to 20-25 nitrates, even with weekly 70% WCs. Granted, I don't keep a super clean tank, but that should give you an idea of the work involved.