Solve for the equation for the indicated variable: 1 over c plus 1 over 5 = 1 over x for x

Solution:
1. Given equation:
\frac{1}{c} + \frac{1}{5} = \frac{1}{x}

2. Find a common denominator for the left-hand side:
- The common denominator for c and 5 is 5c.
- Rewrite the equation: \frac{5}{5c} + \frac{c}{5c} = \frac{1}{x}

3. Combine the fractions on the left-hand side:
\frac{5 + c}{5c} = \frac{1}{x}

4. Cross-multiply to solve for x:
x(5 + c) = 5c

5. Divide both sides by (5 + c) to isolate x:
x = \frac{5c}{5 + c}