17953 ÷ 7 = 2564 R5
Alright, let's work through the division of 17953 by 7 step by step.

Step 1:
7 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 (7) of the dividend behind the 1 and repeat the process: 17 / 7

Step 2:
7 goes into 17 2 times with a remainder of 3.
Write down 2 as next digit of of the result. 
Result so far: 2
Subtract 14 from 17 to get 3.
Bring next digit (9) of the dividend behind the 3 and repeat the process: 39 / 7

Step 3:
7 goes into 39 5 times with a remainder of 4.
Write down 5 as next digit of of the result. 
Result so far: 25
Subtract 35 from 39 to get 4.
Bring next digit (5) of the dividend behind the 4 and repeat the process: 45 / 7

Step 4:
7 goes into 45 6 times with a remainder of 3.
Write down 6 as next digit of of the result. 
Result so far: 256
Subtract 42 from 45 to get 3.
Bring next digit (3) of the dividend behind the 3 and repeat the process: 33 / 7

Step 5:
7 goes into 33 4 times with a remainder of 5.
Write down 4 as next digit of of the result. 
Result so far: 2564
Subtract 28 from 33 to get 5.

The final result is 2564 with a remainder of 5.