Line Check Pilot reported five vehicles drove in front of the aircraft during taxi to the gate. Flight crew took evasive action to avoid collision.

Narrative

I was a LCP (Line Check Pilot) giving a line check to the Captian and FO. While on the ramp we were waiting for an aircraft to clear so we could pull into our gate. When clear we started to turn off the J line towards the gate. At that moment FO yelled STOP Captain stopped the aircraft and FO said there was a vehicle cutting between us and the gate. At that moment I saw the vehicle passing between us and the gate at a very high rate of speed well in excess of what would be a safe speed. (50 mph+). Once it passed FO said he saw another vehicle coming and three more passed inside of us all at a very high rate of speed. Captain and FO did nothing wrong and were following all instructions from the ramp. FO did an excellent job by looking before we turned and possibly prevented a collision between the first vehicle and the aircraft. We were not advised by Ramp or ATC of the vehicles nor I hear any of the vehicles talking to Ramp or ATC. This could have easily resulted in a collision. We need to know why these vehicles were not talking on the radio.