A five gallon is great for one Betta. They prefer warmer water. 80 degrees is good. Since they are a labyrinth fish and that is a delicate organ they should be breathing warm moist air. A cover is a good thing. It will keep the evaporation down and the air above the water surface humid. A small sponge filter is enough and you could even go with a still tank - no filtration or aeration - just a lot of plants.
