Skimmer is used to clean the water in the tank, you can run without one regardless if you have corals but it depends on how you stock and maintain your tank, (water changes)
I have a 60g frag tank with a 10g sump, skimmer not installed yet,this week, I do a 15g water change weekly. I will have all my LPS peices in this tank.
Really depends on how stocked you plan to be and your feeding regimen. If you have plenty of livestock and a couple of messy eaters before long 5 gallons wont be enough of a change to keep params in check