10553 ÷ 6 = 1758 R5
Alright, let's work through the division of 10553 by 6 step by step.

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

Step 2:
6 goes into 10 1 times with a remainder of 4.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 6 from 10 to get 4.
Bring next digit (5) of the dividend behind the 4 and repeat the process: 45 / 6

Step 3:
6 goes into 45 7 times with a remainder of 3.
Write down 7 as next digit of of the result. 
Result so far: 17
Subtract 42 from 45 to get 3.
Bring next digit (5) of the dividend behind the 3 and repeat the process: 35 / 6

Step 4:
6 goes into 35 5 times with a remainder of 5.
Write down 5 as next digit of of the result. 
Result so far: 175
Subtract 30 from 35 to get 5.
Bring next digit (3) of the dividend behind the 5 and repeat the process: 53 / 6

Step 5:
6 goes into 53 8 times with a remainder of 5.
Write down 8 as next digit of of the result. 
Result so far: 1758
Subtract 48 from 53 to get 5.

The final result is 1758 with a remainder of 5.