Will it work? Yes.
Radeon HD 5850 TDP is 151W and suggested PSU is 500W with 2x 6-pin PCIe power connectors.
Though, yor preferred PSU is a Tier three unit.
PSU Tier list:
http://www.tomshardware.co.uk/forum/id-2547993/psu-tier-list.html
Try to get a Tier two unit. I suggest either a Seasonic S12II-520 (80+ Bronze, fully wired, Tier two)
specs: https://seasonic.com/product/s12ii-520/
Or Seasonic M12II-520 EVO (80+ Gold, fully modular, Tier two)
specs: https://seasonic.com/product/m12ii-520-evo/