Tap Water With High-ish Nitrate Reading

Hi all.
my nitrate readings have been 2.5 - 5.0  even after a water change, so I decided to test the tap water and found it was more or less the same.  Nitrite and ammonia readings are good.

I have bought some extra live plants and plan to get some more as soon as I can go to the shop.  Should I be doing anything else?

I agree, 5 ppm is fine. Fish only start to suffer at 20 ppm.

Plants only use nitrate (and nitrite) as a last resort. They prefer ammonia. The reason is simply that nitrite & nitrate have to be converted into ammonia inside the plant, so using ammonia directly takes them less energy.