Some species of algae is normal and expected in a container of water and can be a sign of a healthy system, however, since this is a closed system-even the good algae needs to be removed manually on occasion along with your regular water changes.
You can control it to a degree-first you need to find out what kind of algae it is. Often excess algae is caused by the nutrient load and/or light related.
IMO/E-a 5gal isn't enough space to house other species of fish along with a Betta for algae control. I don't know much about the ADF to know proper housing for them.
Some species of shrimp and snails can help keep some species of algae controlled to a degree, however, IMO they will not rid the tank of all algae-Plus you shouldn't add more livestock to a system unless you can properly keep them, meet their need and you want them to start with.
A closed system will never be able to support them nutritionally and they will need supplement feedings-both add to the bioload.
Lovely setup by the way....