I have this ATI Radeon HD 5670 512 MB graphic card is this a metal support card?

Nope.

If you’re already running with the card on High Sierra, you can directly confirm that in the system configuration.

Details on the check are here:

Install macOS 10.14 Mojave on Mac Pro (Mid 2010) and Mac Pro (Mid 2012) - Apple Support

Radeon HD 7730 and later have GCN, with support for Metal.

No.