To solve the equation \( \frac{1}{1+x} = 5 \), follow these steps:

1. **Isolate the fraction**: The equation is already in a form where the fraction is isolated.
\[
\frac{1}{1+x} = 5
\]

2. **Eliminate the fraction**: To get rid of the fraction, multiply both sides of the equation by \( 1 + x \):
\[
1 = 5(1 + x)
\]

3. **Distribute the 5**: Multiply 5 by each term inside the parentheses:
\[
1 = 5 + 5x
\]

4. **Isolate \( x \)**: Subtract 5 from both sides to isolate the term with \( x \):
\[
1 - 5 = 5x
\]
\[
-4 = 5x
\]

5. **Solve for \( x \)**: Divide both sides by 5 to solve for \( x \):
\[
x = \frac{-4}{5}
\]
\[
x = -\frac{4}{5}
\]

So, the solution to the equation \( \frac{1}{1+x} = 5 \) is \( x = -\frac{4}{5} \).