Hello Georgios,
Activitysuper has a good point about choosing some of the best ones as testimonials for conversion rate optimization.
However, there is a chance you could get the third-party review data supplier to noindex their version of the reviews/content. It depends on what your contract says. If I was paying a company to handle the reviews for my product, like a BazaarVoice for example, I'd expect to have exclusive rights to that content.
To be specific though, we'll need more information. Where will these reviews go? If it would be 5,000 new pages of duplicate content, that's an issue. If they would be put onto product pages there are many options. You could put them in an iframe so you show the content to users but avoid the duplicate content issue. You could show the best three or four on the product page and then show the rest on a separate page that you don't allow to be indexed.
You are asking a great question, but I think some more information is necessary in order for anyone to definitively answer it.