Java moss usually does not need lots of light. If you put it in a jar with more light there would be not enough nutrients. What is your "K" rateing of your lights?? Should be between 6500 and 10000.
Mine did the same thing. Its just debri from the tank. When I added my cherry shrimp to the tank they cleaned it out. Try adding 1 or two shrimp. If you think your beta might turn them into a snack you could try pulling the moss out of your tank and putting it into a bowl with acouple of shrimp to clean it. When its done put the shrimp back where you got them and put the moss back in the tank. If you don't already have shrimp buy a couple of ghost shrimp, they are cheap and will clean it too.
My moss looked like that for a little bit when i had it in a 5 gallon with no grow light. Switched out the bulb and put some of it in my 20long with good lighting and it has made a great comeback. I honestly thought it was long gone when i tried to bring it back, but within a few days i noticed green tips appearing again. It seems to be a tough little plant to kill.
java moss needs just a bit more light than a couple other plants. in my 50 gal it's my borderline plant that just dies back. my 30 has just a smidge (technical term) more light and it grows like wildfire.
that being said 23 watts over 5 gals is way more than enough. maybe it's time to change your bulb or adjust your dosing.