Find the value of x given the diagram with two parallel lines intersected by two transversals, forming angles 5x and 3x, and an angle of 136 degrees.

Draw a line through the vertex of the $136^\circ$ angle, parallel to the two given parallel lines. This auxiliary line divides the $136^\circ$ angle into two smaller angles. Let's call the upper part $\alpha$ and the lower part $\beta$.
So, $\alpha + \beta = 136^\circ$.

For the left transversal line, the angle $5x$ and the upper part $\alpha$ are alternate interior angles. Since the lines are parallel, alternate interior angles are equal.
Therefore, $\alpha = 5x$.

For the right transversal line, the angle $3x$ and the lower part $\beta$ are alternate interior angles. Since the lines are parallel, alternate interior angles are equal.
Therefore, $\beta = 3x$.

Substitute the expressions for $\alpha$ and $\beta$ into the equation from Step 1:

Divide both sides by 8 to find the value of $x$:

The value of $x$ is 17.