Given that $g(x)$ has a $y$-intercept at $(0, 5)$, this means that:

$g(0) = 5$

Now, we are asked to find the $y$-intercept of $g(12x)$. To find the $y$-intercept of a function, we set $x = 0$ in the function. So, for $g(12x)$:

$g(12(0)) = g(0)$

Since we know $g(0) = 5$, it follows that:

$g(12(0)) = 5$

Thus, the $y$-intercept of $g(12x)$ is also at $(0, 5)$.

The correct answer is:

B. (0, 5)

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Do you need further details or have any other questions?

Here are five related questions:

1. What happens to the graph of $g(x)$ when transformed to $g(12x)$?
2. How does a vertical stretch or compression affect the $y$-intercept of a function?
3. What would happen to the $y$-intercept if the function were $g(x/2)$?
4. How do horizontal transformations affect the shape of a graph?
5. Why is the $y$-intercept unchanged by horizontal compressions or stretches?

Tip: Horizontal transformations do not affect the $y$-intercept, as they only impact how the function behaves along the $x$-axis.