1. **State the problem:** We need to find the value of $x$ that makes lines $A$ and $B$ parallel by using the property of same side exterior angles. 2. **Recall the rule:** When two lines are cut by a transversal, if the same side exterior angles are supplementary (sum to 180°), then the lines are parallel. 3. **Set up the equation:** The two same side exterior angles given are $(5x)^{\circ}$ and $150^{\circ}$. According to the rule: $$5x + 150 = 180$$ 4. **Solve for $x$:** $$5x + 150 = 180$$ Subtract 150 from both sides: $$5x + \cancel{150} - \cancel{150} = 180 - 150$$ $$5x = 30$$ Divide both sides by 5: $$\frac{5x}{\cancel{5}} = \frac{30}{\cancel{5}}$$ $$x = 6$$ 5. **Conclusion:** The value of $x$ that makes lines $A$ and $B$ parallel is $6$.