Start with the graph of $f(x)=5^{x}$. Then write a function $g(x)$ that results from the given transformation. shift $f(x) 7$ units downward
\[
g(x)=
\]

Step 1 ：Understand the problem: The problem is asking to shift the function $f(x)=5^{x}$ 7 units downward. This means we need to subtract 7 from the function.

Step 2 ：Write the new function: The new function $g(x)$ is obtained by subtracting 7 from $f(x)$. So, $g(x) = f(x) - 7$.

Step 3 ：Substitute $f(x)$ into the equation: We know that $f(x) = 5^{x}$, so we substitute this into the equation to get $g(x) = 5^{x} - 7$.

Step 4 ：Simplify the function: The function $g(x) = 5^{x} - 7$ is already in its simplest form.

Step 5 ：Check the result: The function $g(x) = 5^{x} - 7$ is the graph of $f(x) = 5^{x}$ shifted 7 units downward, which is what the problem asked for.

Step 6 ：The final answer is $g(x) = 5^{x} - 7$.