-5¾ divided by -5 is the same as 5¾ divided by 5, because a negative divided by a negative is positive.
We change 5¾ to an improper fraction by converting the whole number 5 into quarters by multiplying 5 by 4=20 quarters (just as there are 20 quarters in $5), then we add the extra 3 quarters making 23 quarters or 23/4. To divide by 5 we multiply the denominator by 5=23/20. This is an improper fraction so we convert 20 twentieths into 1 whole and 3 twentieths remaining: 1³⁄₂₀.