Way to keep track of rounds during a while loop

So I'm trying to keep track of what is played in a round by each player and who wins each round in my R/P/S program. Is there a way to do that in a, possibly, infinitely repeating loop? Here's the code

import random
Round = 0
Player_Score = 0
Computer_Score = 0
while Player_Score < 5 and Computer_Score < 5:
    Player_object = input("Would you like to choose R, P, or S?")
    Computer_object = random.sample("RPS", 1)[0]
    if Player_object == "R" or Player_object == "r":
        if Computer_object == "R":
             print("You have chosen " +Player_object+ " and the Computer chose " +str(Computer_object)+ ".You have tied with the Computer and neither of you have scored a point.")
        elif Computer_object == "P":
            Computer_Score += 1 
            print("You have chosen " +Player_object+ " and the Computer chose " +str(Computer_object)+ ". You have been beaten by the Computer and it has scored a point.")
        else:
            Player_Score += 1
            print("You have chosen " +Player_object+ " and the Computer chose " +str(Computer_object)+ ".You have beaten the Computer and you have scored a point.")


    if Player_object == "P" or Player_object == "p":
        if str(Computer_object) == "R":
            Player_Score += 1
            print("You have chosen " +Player_object+ " and the Computer chose " +str(Computer_object)+ ".You have beaten the Computer and you have scored a point.")
        elif str(Computer_object) == "P":
           print("You have chosen " +Player_object+ " and the Computer chose " +str(Computer_object)+ ". You have tied with the Computer and neither of you have scored a point.")
        else:
            Computer_Score += 1
            print("You have chosen " +Player_object+ " and the Computer chose " +str(Computer_object)+ ".You have been beaten by the Computer and it has scored a point.")


    if Player_object == "S" or Player_object == "s":
        if str(Computer_object) == "R":
             print("You have chosen " +Player_object+ " and the Computer chose " +str(Computer_object)+ ".You have been beaten by the Computer and it has scored a point.")
        elif str(Computer_object) == "P":
            Computer_Score += 1
            print("You have chosen " +Player_object+ " and the Computer chose " +str(Computer_object)+ ". You have beaten the Computer and you have scored a point.")
        else:
            Player_Score += 1
            print("You have chosen " +Player_object+ " and the Computer chose " +str(Computer_object)+ ".You have tied with the Computer and neither of you have scored a point.")
if Computer_Score == 5 and Player_Score != 5:
    print("The Computer has won!")
if Player_Score == 5 and Computer_Score != 5:
    print("You have won and beaten the computer")
R = "Rock"
r = "Rock"
P = "Paper"
p = "Paper"
S = "Scissors"
s = "Scissors"