What live plant should I add to my betta tank?

Water Sprites work great for Bettas! I reccomend them.

A 5 gallon tank is small enough that many plants will work as a large centerpiece. Nerite Snails will not eat plants. They'll remove algae from plant leaves, but won't hurt the plants themselves. I've had them in a few of my planted aquascapes and they've worked out well. 

Bettas need to reach the surface to breathe, so make sure that at least 1/3 of the total surface is open water.

Water Sprite (Ceratopteris thalictroides), Pennywort (Hydrocotyle leucocephala), and Green Cabomba (Cabomba caroliniana) can all be planted in your gravel and will grow up and then across the surface. They do best with an aquarium fertilizer like Flourish Comprehensive added to the water column, and moderately bright light.

If you are looking for one plant that will basically fill the tank, Ruffled Swords (Aponogeton crispus) can get really large and will provide lots of hiding places. You can trim off the larger leaves at their base to keep it a manageable size for a 5 gallon.

You could also try Amazon Frogbit (Limnobium Laeviatum). This is actually a floating plant that has long roots that will go down toward the mid level of the aquarium. Frogbit does best with aquarium fertilizer added to the water column. If you have success with Frogbit, you might also want to try the more high maintenance Dwarf Water Lettuce (Pistia stratioes), which has even longer and more feathery roots and which, in my experience, is the favorite plant of Bettas by far. It requires steady liquid fertilizer dosing and fairly high lighting, though.

Here are 22 of the best live plants for betta fish tanks:

Amazon Sword. The broad leaves of the Amazon Sword make it a favorite among Betta fish. ...

Anubias Nana. If you are searching for the perfect Betta fish plant, look no further. ...

Marimo Moss Balls. ...

Java Fern. ...

Water Sprite. ...

Java moss. ...

Anacharis. ...

Pennywort.

The very best plant for a betta is the java fern!! You attach it to a piece of driftwood. Low-level light is fine for java fern, an easy plant.

Stem plants maybe like rotala, ludwigia and anacharis. They get tall and will need trimming. You can then plant the trimmings. You can plant them right in the gravel but you will need root tabs.

You could get epiphyte plants. Those are plants that you do not plant in the gravel. They get nutrients from the water so you would add a liquid fertilizer. You can attach these to drift wood, rocks or any decorations. You can use cyanoacrylate super glue or thread to attach them. Java ferns get tall for a 5 gallon so that might be a good choice. Anubias and bucephalandra are also good choices. They are hardy plants. 

Snails don't generally eat healthy plants. If you find they are eating your plants its because the plant is already dying. 

Elodea grows quickly and can survive some chewing from the fish. 

There is a books worth of information you need to know in order to do All that.

A simple idea is to get some driftwood and tie some anubias too it, you dont plant the roots, it will die if you do.  so with a propper day night lighting cycle you could create strips of anubias.  It may not have the hight you want , sword plants are slightly more demanding, but can by planted in the gravel.

https://www.aquariumcarebasics.com/aquarium-plants...

I read that Nerite snails are the one snail that leaves plants alone.  But I have never had plants and nerites at the same time.

Do not block the surface of the tank with plants.  Bettas need to get to the surface of the water to breath.  So beware those peacelilly plants said to be great with betas!

whatever one you want to add to it