Hi spacecollective,
Maybe I shoud've provded more context around my response.
I'm assuming that your h5 tag would be something like "Product Description" which is a very common reason amongst ecommerce sites as to why they have duplicate header tags across all their product pages. If this is the case, you don't have to worry about it. You wouldn't need to rank for something like "Product Description" anyway.
If this is not the case, maybe you could provide a URL to your page or examples of header tags that you're using?
Jac