5667 ÷ 8 = 708 R3
Alright, let's work through the division of 5667 by 8 step by step.

Step 1:
8 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 (6) of the dividend behind the 5 and repeat the process: 56 / 8

Step 2:
8 goes into 56 7 times with a remainder of 0.
Write down 7 as next digit of of the result. 
Result so far: 7
Subtract 56 from 56 to get 0.
Bring next digit (6) of the dividend behind the 0 and repeat the process: 6 / 8

Step 3:
8 goes into 6 0 times with a remainder of 6.
Write down 0 as next digit of of the result. 
Result so far: 70
Subtract 0 from 6 to get 6.
Bring next digit (7) of the dividend behind the 6 and repeat the process: 67 / 8

Step 4:
8 goes into 67 8 times with a remainder of 3.
Write down 8 as next digit of of the result. 
Result so far: 708
Subtract 64 from 67 to get 3.

The final result is 708 with a remainder of 3.