Hi Patrick,
Looks like no, maybe in eGPU enclosure?...
Again, the card supports PCIe 4.0 connections, though it will work with any PCIe 3 slots in the Mac Pro or in eGPU enclosures. It is also a single-width, full-height card.
https://appleinsider.com/articles/20/02/10/amd-radeon-pro-w5500-offered-as-price-conscious-alternative-mac-pro-gpu
2012 Mac Pro...
Expansion includes two external 5.25" "optical" bays (one free by default), four internal 3.5" "cable-free, direct attach" hard drive bays (three free by default), and four PCIe 2.0 slots (one free PCIe 2.0 x16 slot and two free PCIe 2.0 x4 slots with the default single graphics card installed).
https://everymac.com/systems/apple/mac_pro/specs/mac-pro-quad-core-3.2-mid-2012-nehalem-specs.html