I assumed that you just had the 5gal and no other equipment :P. On that route, Siamese fighting fish are the most common fish available that is "suitable" for an unfiltered, unheated system of that volume.
Other fish that will do well are killifish. Rarely will you find them at the LFS. One can get addicted to this family of fish as the reproductive cycle and egg handling is fascinating. Depending on the species, the eggs are so hardy, ppl mail them to each other. Going this route is akin to kids collecting and trading Pokemon doo-dads and you'll have a wall unit full of 2.5-5gal aquariums.
With a filter, it opens up to more options of fish and critters to put in but limited to the size of the aquarium.
Going with live plants, one has to consider 3 factors:
1. light requirement
2. nutrient demand (foliar/leaf and root uptake)
3. growth rate
Uber easy aquatic plants are Java Fern and Java Moss; don't require much light nor nutrient.
Stemmed plants grow fast and in turn have a relative high nutrient demand for nitrogen and phosphorous. Red leafed stemmed plants require more light and iron as well as dissolved CO2/carbon source. When they get too tall, you have to yank them out, trim from the bottom and replant. Trimming from the top will be ok for the first few trimmings but overtime, the older leaves on the lower stems will die off and the lower node where you trim will develop two stems and get a more bushy top appearance.
"Crowned/rosette" plants send leaves out from a central point. As more leaves develop from the centre, the older leaves get pushed radially outwards, ie Amazon sword plant. Can't do much about the height but you can control the breath of foliar growth buy trimming the outer leaves. Others send up 2-4 leaves and send runners to create a daughter plant. Some stay short, ie Cryptocoryne plants and some can grow to the surface to a point that it lays flat across the surface, ie Valisinaria sp.. Trimming Vals is like cutting hair...snip, snip
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Not sure where you live but maybe there is an aquarium club that you can attend. Fish heads are a friendly bunch
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