To find the range of the function $f(x) = 2^{12x} - 5$, let's break it down:

1. Base Function: The expression $2^{12x}$ is an exponential function, where $2^y > 0$ for all real values of $y$. The exponential function grows rapidly but is always positive, meaning $2^{12x} \in (0, \infty)$.

2. Shifted Function: The function is then shifted down by 5 units. Therefore, the smallest value of $2^{12x}$ (which is 0) will map to $-5$, and as $2^{12x}$ grows, the function will approach $\infty$.

Thus, the range of $f(x) = 2^{12x} - 5$ is: $\boxed{(-5, \infty)}$

Would you like a deeper explanation of how this works? Here are some related questions:

1. What is the general form of an exponential function?
2. How does shifting a function vertically affect its range?
3. Can an exponential function ever equal zero?
4. What are the effects of horizontal scaling in $2^{12x}$?
5. How do you find the domain and range of other types of functions?

Tip: When working with exponential functions, keep in mind that their range is always positive, and any vertical shifts directly affect the minimum or maximum values.