You have the following expression:
[tex]\lvert5x-8\rvert+5=32[/tex]subtract 5 both sides of the equation:
[tex]\begin{gathered} \lvert5x-8\rvert=32-5 \\ \lvert5x-8\rvert=27 \end{gathered}[/tex]Take into account that the absolute value of any number is equal to the same number but positive.
Then, you have:
[tex]5x-8=-27[/tex]and
[tex]5x-8=27[/tex]Then, solve the previous equations:
5x - 8 = -27 add 8 both sides
5x = -27 + 8
5x = -19 divide by 5
x = -19/5
5x - 8 = 27 add 8 both sides
5x = 27 + 8
5x = 32 divide by 5
x = 32/5
Then, the solutions of the given equations are:
x = -19/5
x = 32/5
