I'm not sure where I would go in order to get a new fan let alone how to safely get the fan out and put a new one in.
You need to contact the card manufacturer for replacement parts/advice.
Since you didn't write which exactly 290x you have, I can't link you directly to an example search result.
Look at what model and manufacturer you have, and write that model and manufacturer with a "fan" word at the end into aliexpress or ebay searches.
For example look for:
Vapor X 290x sapphire FAN
If you want to be ultra sure about the same type of fans, take your fans off and look at their underside. They will have something like:
Brushless Fan 5V type ABC123456X on their sticker, this is the type of fans you need to look for.
Other fans with the same voltage and size should fit just fine. Most often these are sold as fan sets (a set of two or three) because their power cords are shared.
Be careful not to take off the card radiator if it has thermopads, because you will have to replace these along with thermal paste, if you do.
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