59001 ÷ 7 = 8428 R5
Alright, let's work through the division of 59001 by 7 step by step.

Step 1:
7 goes into 5 0 times with a remainder of 5.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 5 to get 5.
Bring next digit (9) of the dividend behind the 5 and repeat the process: 59 / 7

Step 2:
7 goes into 59 8 times with a remainder of 3.
Write down 8 as next digit of of the result. 
Result so far: 8
Subtract 56 from 59 to get 3.
Bring next digit (0) of the dividend behind the 3 and repeat the process: 30 / 7

Step 3:
7 goes into 30 4 times with a remainder of 2.
Write down 4 as next digit of of the result. 
Result so far: 84
Subtract 28 from 30 to get 2.
Bring next digit (0) of the dividend behind the 2 and repeat the process: 20 / 7

Step 4:
7 goes into 20 2 times with a remainder of 6.
Write down 2 as next digit of of the result. 
Result so far: 842
Subtract 14 from 20 to get 6.
Bring next digit (1) of the dividend behind the 6 and repeat the process: 61 / 7

Step 5:
7 goes into 61 8 times with a remainder of 5.
Write down 8 as next digit of of the result. 
Result so far: 8428
Subtract 56 from 61 to get 5.

The final result is 8428 with a remainder of 5.