since you know x is between 4 and 5, lets start in the middle using 4.5 for x
4.5^3 - 5(4.5) = 68.625 ( this is larger than 59, so we know the number is less than 4.5)
lets try 4.2: 4.2^3 -5(4.2) = 53.088 ( this is smaller than 59, so we know the number is larger than 4.2)
4.3: 4.3^3 -5(4.3) = 58.007
4.4: 4.4^4 -5(4.4) = 63.184
so we know the answer is between 4.3 and 4.4
4.32: 4.32^3 - 5(4.32) = 59.02 round to 59.0 ( to 1 decimal place)
I think this is what the teacher wants for an answer.