5,000 visitors per day is pretty good for a health related blog or any blog.
With 5,000 visitors per day you should certainly get a payout each month from Adsense.
Health related niches usually pay pretty good Via Adsense so you could likely earn from $40.00 to $50.00 per day and maybe even $100.00 per day depending on the CTR of the website on the ads.
The more clicks you get the more money you get.
So assuming all those 5,000 visits to your website are real visits then you can certainly be earning some money.
You could also potentially make more than just Adsense by promoting affiliate products and services in the health related niche.