1. The problem asks to identify whether the asymptote of the function $f(x) = 3 \left(\frac{1}{2}\right)^x - 5$ is vertical or horizontal. 2. The general form of an exponential function is $f(x) = a b^x + c$, where $a$ and $b$ are constants and $c$ shifts the graph vertically. 3. For exponential functions of this form, the horizontal asymptote is the line $y = c$. 4. In this function, $c = -5$, so the horizontal asymptote is $y = -5$. 5. There is no vertical asymptote for this function because exponential functions are defined for all real $x$. 6. Therefore, the asymptote is horizontal, not vertical. Final answer: The asymptote is horizontal at $y = -5$.