To find \( f(1) \) using the function rule \( f(x) = -7(5)^x - 3 \), we need to substitute \( x = 1 \) into the function.
\[ f(1) = -7(5)^1 - 3 \]
Now, calculate \( (5)^1 \):
\[ (5)^1 = 5 \]
Now substitute this back into the equation:
\[ f(1) = -7(5) - 3 \]
Now perform the multiplication:
\[ -7(5) = -35 \]
Now, substitute this value back into the equation:
\[ f(1) = -35 - 3 \]
Now perform the final subtraction:
\[ f(1) = -38 \]
Thus, the value of \( f(1) \) is:
\[ \boxed{-38} \]