Yepp, you and sixty are right: Cyanobacteria of some kind (see
page 3, post #52).
In a 5 month old tank they are quite a common sight and could still be considered part of the "ugly phase". Many people get dinoflagellates or cyano mats within the first year. The exact cause is somewhat disputed.
In the past people assumed high nitrate and phosphate to be the main culprit, but this viewpoint seems to be becoming less popular and might be an oversimplification.
By now dissolved organic carbon (DOC), or rather overall "organics", are blamed. We don't know too much about them, but if you have ever looked into "carbon dosing", the effect of supplying organic carbon to a tank on bacteria growth becomes visible very fast. It usually doesn't end in cyanobacteria outbreaks though, so whether that is already the whole story is difficult to say.
Either way, water changes combined with manual removal are still one of the go-to approaches. This more or less pleases both viewpoints:
You are reducing nitrate and phosphate for the people that still hold on to the original belief that "nitrate and phosphate" are to blame, and you are also removing organics from the system, so you are covered on that front too.
Some people also try dosing
Synechococcus spp., which is basically a planktonic cyanobacterium that doesn't form mats and therefore won't cause issues in reef tanks. It's supposed to "outcompete" mat forming species for nutrients, but I would still consider it a rather experimental approach that you can give a try if you can find someone selling it. Alternatively, many people dose bottled bacteria products, which is just as experimental in my opinion, but also worth a try if the mats persist for another month or two despite frequent manual removal.
As your tank is very young I would avoid antibiotics for now. Those will inevitably affect the "good" bacteria as well and instead of cyanobacteria some other nuisance might take over instead.
