51637 ÷ 5 = 10327 R2
Alright, let's work through the division of 51637 by 5 step by step.

Step 1:
5 goes into 5 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 5 from 5 to get 0.
Bring next digit (1) of the dividend behind the 0 and repeat the process: 1 / 5

Step 2:
5 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 10
Subtract 0 from 1 to get 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 5

Step 3:
5 goes into 16 3 times with a remainder of 1.
Write down 3 as next digit of of the result. 
Result so far: 103
Subtract 15 from 16 to get 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 5

Step 4:
5 goes into 13 2 times with a remainder of 3.
Write down 2 as next digit of of the result. 
Result so far: 1032
Subtract 10 from 13 to get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 5

Step 5:
5 goes into 37 7 times with a remainder of 2.
Write down 7 as next digit of of the result. 
Result so far: 10327
Subtract 35 from 37 to get 2.

The final result is 10327 with a remainder of 2.