Performance of DAM is overall slow so we upgraded it to 6.5 latest version and still we are facing the issue of slowness. Please suggest some ways to improve the performance and we are also following all the best practices suggested by Adobe.
Hope you are doing well!
Please refer to this -
It might help!
What does slowness mean to you? It is very subjective...
Capture a series of thread dumps while things are 'slow' and use that as a starting point to better understand WHY it's slow. 
- could be a product issue
- could be an index issue -- eg a corruption, or perhaps heavy usage of apache tika that's performing full-text extraction on some large number of assets in some remote datastore
- could be an implementation issue
From there we can better guide you .. but it could be anything without knowing more specific information.
First of all check for the unused assets in your site structure and try to keep as many assets that are required for the sites.
As most of time we keep on adding the images and videos to DAM and it makes it content heavy.
I have some Groovy scripts which can help you out to do so : Groovy scripts on AEM