$$ \int _ { 1 } ^ { 5 } \frac { 1 } { x } dx , F ( x ) = \ln ( x ) $$

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1. We start with the integral:
   $$
   \int_{1}^{5} \frac{1}{x} \, dx
   $$

2. The antiderivative of $$\frac{1}{x}$$ is:
   $$
   \int \frac{1}{x} \, dx = \ln |x| + C
   $$
   Given that $$ F(x) = \ln(x) $$ is an antiderivative, we proceed to the next step.

3. Evaluating the definite integral from $$ x = 1 $$ to $$ x = 5 $$, we have:
   $$
   \int_{1}^{5} \frac{1}{x} \, dx = \ln(5) - \ln(1)
   $$

4. Since $$\ln(1) = 0$$, the expression simplifies to:
   $$
   \ln(5) - 0 = \ln(5)
   $$

Thus, the value of the integral is:
$$
\ln(5)
$$
The value of the integral is $$ \ln(5) $$.

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