ANSWER
x=-2
EXPLANATION
The given polynomial function is:
[tex]f(x) = {(x - 5)}^{3} {(x + 2)}^{2} [/tex]
The polynomial has two factors, one with an odd multiplicity which is
[tex] {(x - 5)}^{3} [/tex]
and the other with an even multiplicity which is
[tex] {(x + 2)}^{2} [/tex]
The graph does not cross the x-axis at where the multiplicity is even.
Therefore the graph touches the x-axis at
[tex]x = - 2[/tex]
We got this by solving
[tex]{(x + 2)}^{2} = 0[/tex]
