To solve this equation, we need to follow the order of operations $PEMDAS$:

Step 1: Solve the multiplication inside the parentheses:
5$3$ = 15
13$2$ = 26

Step 2: Add the results from step 1:
15 + 26 = 41

Step 3: Divide the result of step 2 by 21:
41 / 21 = 1.95238095238

Step 4: Multiply the result of step 3 by 180:
1.95238095238 * 180 = 351.428571429

Step 5: Subtract 47700 divided by 45 from the result of step 4:
351.428571429 - $47700/45$ = 351.428571429 - 1060 = -708.571428571

Step 6: Add 4946 to the result of step 5:
-708.571428571 + 4946 = 4237.42857143

Therefore, the final answer is approximately 4237.429.