Yes, Nicola, your coin is of the same type as the coin in the first link you provided. (The second link is messed up, I think...it's taking me to a silver tetradrachm of Tiridates of Parthia)
No, the Phraates of your coin is not Phraates V (Phraataces) from Parthia. Your coin was minted more than a hundred years later. The following is from the essay that Echizento linked to (from page seven):
"Around 25 BC an Arsacid (Parthian) line began to rule Elymais and, accordingly, we begin to recognize Parthian names of some kings and to see the appearance of Parthian-type tiaras on the portraits of several of these rulers"
So the rulers of Elymais who had Parthian names like Phraates and Orodes were probably blood relatives of the Arsacids (the ruling line of Parthia) but they were not the same Orodes and Phraates as the Parthian kings.
It's always a pleasure to see coin from Elymais posted here. If you pick up more in the future, be sure to show them to us. Thanks for sharing.