I would just gently run your fingers along the leaves of your plant, as this is what i do with my anubis plants and it seems to work with getting the black hair algae off easily.
As for the Moon rock, its normal for rocks to get algae on them, i would get a snail(mystery, apple, or nerite snail) as they can help with cleaning in the hard places as well as glass cleaning(depending on the type of algae you have). Or you could test your water parameters, this could also help us determine why your small tank is growing algae, Also what tank light are you using and how long your lights are on(depending on the light type it may be best to have it one for 8-10 hours(12 at most if its a low wattage)). Within your tank is it situated, is any natural light hitting it during the day(Sunlight, either directly or indirectly hitting the tank(bouncing off of a window into your room where the tank is situated))..
Do you add anything into the tank that contains a large amount of phosphorus, as i know this can cause algae to grow. As well as is their a current in your tank from your 5Gal filter(i would assume thats the filter you have), Also, do you do your water changes(atleast 25% but no more than 75% for a 5Gal tank) a couple times a week or daily?(do you also syphon your substrate(Gravel/sand or a mix of the 2)).
But mostly what are your water parameters( if you dont have a test kit, i would suggest you go and get one from your LFS so that we may help you further