88114 ÷ 7 = 12587 R5
Alright, let's work through the division of 88114 by 7 step by step.

Step 1:
7 goes into 8 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 7 from 8 to get 1.
Bring next digit (8) of the dividend behind the 1 and repeat the process: 18 / 7

Step 2:
7 goes into 18 2 times with a remainder of 4.
Write down 2 as next digit of of the result. 
Result so far: 12
Subtract 14 from 18 to get 4.
Bring next digit (1) of the dividend behind the 4 and repeat the process: 41 / 7

Step 3:
7 goes into 41 5 times with a remainder of 6.
Write down 5 as next digit of of the result. 
Result so far: 125
Subtract 35 from 41 to get 6.
Bring next digit (1) of the dividend behind the 6 and repeat the process: 61 / 7

Step 4:
7 goes into 61 8 times with a remainder of 5.
Write down 8 as next digit of of the result. 
Result so far: 1258
Subtract 56 from 61 to get 5.
Bring next digit (4) of the dividend behind the 5 and repeat the process: 54 / 7

Step 5:
7 goes into 54 7 times with a remainder of 5.
Write down 7 as next digit of of the result. 
Result so far: 12587
Subtract 49 from 54 to get 5.

The final result is 12587 with a remainder of 5.