It should work.  As you can see from the big auction site, most if not all power supplies for for T5810, T7810, and T7910 are being claimed as cross reference compatible in their listings https://www.ebay.com/sch/i.html?_from=R40&_trksid=p4432023.m570.l1313&_nkw=precision+5810+power+supply&_sacat=0

You still need to have a compatible power extender board with x2 graphics output with 8-pin connector cables.