Hey there! Welcome to Tropical Fish Keeping! And congrats on your first tank :) My first tank was a 5 gallon as well! Hahaha. First, a couple of questions for you. How long have you setup and cycled the tank for? If you're unsure on what a tank cycle/how to cycle a tank, you can go to this thread A Beginner's Guide to the Freshwater Aquarium Cycle
here. It'll explain what a cycle is, and what you can do to start the cycle.
Usually for a 5 gallon tank, its good enough only for 1 betta, or a small shoal of smaller fish, such as guppies. Ottos usually need a larger tank, and one that's been established for a little while so they'll have algae to eat not just on the leaves, but on and around the tank as well. Also, bettas are aggressive fish, and territorial to a degree, so mixing some fish with a betta isn't recommended. Some smaller tetras are also quite good starter fish as well, and both guppies and tetras are visually pleasing to look at.
I believe those plants you have are Anubias
plants. They're a great beginner plant, as they are low maintenance and are very hardy; you don't need plant fertilizers nor lots of light for these plants to do well. However, one thing you do need to watch out for is that you do not want to plant them underneath the substrate *gravel* as this would cause them to rot. You can anchor it to a rock, or leave it free floating. In terms of the black spots, it could be algae, but I'm not sure. If you're worried, you can buy a snail or get some for free at your local fish store, *petsmart is having a sale on mystery snails for a dollar each, pretty decent deal* and contrary to popular belief, snails DO NOT eat your plants; they only eat on the layer of algae growing on plant leaves, or decaying/dead plant matter, so don't worry about pest snails :) They, for the most part, are all beneficial *until they take over your tank, aka 100 snails in your tank, then you can worry :D*
In terms of the filter, it looks like a marina internal filter, not sure on which model. But assuming if its the smallest one, it should be good enough, as their smallest filter is rated for 6.6 gallons I believe. Since we're on the subject of equipment, do you have a water heater? I'm not sure on how the temperature gets in your neck of woods, but having an adjustable water heater will help regulate the temperature of your tank, and prevent large fluctuations, which can stress and potentially kill your fish. Also, do you plan on having an air stone with a pump? It's good to have those handy as it'll help the process of getting oxygen in the water for your fishies :)
Anyways, hope this helps, and welcome to Tropical Fish Keeping! And feel free to ask as many questions as you need; that's what we're here for!