Had a deep cleaning 5 month ago, I still got a gum inflammation and I've got a tooth coming though. I use toothpaste and mouthwash why won't it go.

See your dentist . If inflammation is coming back, you need to see the dentist again. In general you should be seeing him every 3 month until he can put you on a 6 month recall system. This can be due to several factors but You must brush ( 3 times a day) and floss regularly at bed time and some patients may have resistant bacteria and may need additional or other treatment.
Gum inflammation. It's very important to pay attention to your gums. Gums play a major role not only in your dental health, but in your general health. Regardless, the cause of gum inflammation, there are steps you can take to minimize gum damage:see your dentist every 3 month, brush and floss properly 2X/day, drink water, eat well-balanced diet and relax.