ANSWER
[tex]y = - 5[/tex]
EXPLANATION
The horizontal asymptote of a general exponential function,
[tex]f(x) = a {(b)}^{x} + c[/tex]
is y=c.
The given exponential function is
[tex]f(x) = 4{(2)}^{x} - 5[/tex]
By comparing the given function to
[tex]f(x) = a {(b)}^{x} + c[/tex]
we have c=-5, therefore the horizontal asymptote is
[tex]y = - 5[/tex]
