seemingly simple problem i just cant seem to solve

sqrt(x+5)-sqrt(8-x)<=1

x>=5

x<=8

because of the square roots, i can assume that all numbers are possitive so i can open up by multiplying by the power of 2

x+5-2*sqrt(x+5)(8-x)+8-x<=1

therefore

12<=2*sqrt(x+5)(8-x)

divide by 2 and then again power of 2-to get rid of the sqrt

36<=3x+40-x^2

now i solve it and i get -1<=X<=4 every time but the solution is -5<=x<=4

what am i doing wrong??

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Additional Details

the answer is any x between -5 and 4, it is the right answer but i dont know how to get to it...

i can only get from -1 to 4, but if you put any x till -5 it works, how do i solve this