To solve the equation \( 39 \cdot (x - 5) = 35 \), follow these steps:

1. **Distribute**: Start by distributing the \( 39 \) on the left side of the equation.
\[
39x - 195 = 35
\]

2. **Add 195 to both sides**: To isolate the term with \( x \), add \( 195 \) to both sides.
\[
39x = 35 + 195
\]
\[
39x = 230
\]

3. **Divide by 39**: Next, divide each side by \( 39 \) to solve for \( x \).
\[
x = \frac{230}{39}
\]

4. **Simplify (if possible)**: The fraction \( \frac{230}{39} \) does not simplify further, so the answer is:
\[
x \approx 5.897
\]

Thus, the solution to the equation \( 39 \cdot (x - 5) = 35 \) is
\[
x = \frac{230}{39} \text{ or approximately } 5.897.
\]