What is the equation for the asymptote of the following function? f(x)=-2^-x+5

Assuming that the given function is - 2 ^ (- x + 5) you need to find the limit of the function as x goes to negative infinity.

That is:

Lim x → ∞ of [ - 2^ ( - x + 5) ]

And the result is 0, meaning that the asymptote is y = 0.

You can observe the graph in the attached picture.