Does Mac Pro 5,1 support USB 3?
No the first Mac Pro with a USB 3 port is the latest (6.1, late 2013)

From the specifications for your particular Mac Pro:


  Connections and audio
  
  
  Four FireWire 800 ports (two on front panel, two on back panel)
  Five USB 2.0 ports (two on front panel, three on back panel)
  Two USB 2.0 ports on included keyboard
  Front-panel headphone minijack and internal speaker
  Optical digital audio input and output TOSLINK ports
  Analog stereo line-level input and output minijacks
  Multichannel audio through Mini DisplayPort
  


A quick Google search shows several PCI Express USB 3.0 cards, e.g.,


Sonnet Allegro USB 3.0 PCIe
CalDigit SuperSpeed PCI Express Card
HighPoint RocketU card