I'm wondering if it might be cheaper to get, say, a new GT 1030 with passive cooling. It's not quite as good a performer as the HD 5870, but at only 30W, there are multiple variants with silent cooling solutions.
Beware of the DDR4 variants, though, as they seem to charge as much for those as they do for the better GDDR5 versions.
I don't know how much a waterblock that would fit the 5870 would go for, though.