To determine the value of $x$ that will make lines $l$ and $m$ parallel, we need to use the properties of parallel lines and transversals. Specifically, we can use the concept of corresponding angles, which must be equal for the lines to be parallel.

In the given diagram, angle $60^\circ$ and angle $x - 5^\circ$ are corresponding angles. Therefore, for lines $l$ and $m$ to be parallel, these corresponding angles must be equal.

So, we set up the equation: $x - 5 = 60$

Solving for $x$: $x - 5 = 60$ $x = 60 + 5$ $x = 65$

Therefore, the value of $x$ that will make the lines $l$ and $m$ parallel is $65^\circ$.

If you want more details or have any questions, feel free to ask. Here are some related questions that expand on this information:

1. What are corresponding angles and how are they identified?
2. How can alternate interior angles be used to determine if two lines are parallel?
3. What is the definition of a transversal in geometry?
4. How can you use the concept of supplementary angles to solve for unknown angles in parallel line problems?
5. What are the properties of alternate exterior angles?
6. How do you prove two lines are parallel using geometric postulates or theorems?
7. What role do vertical angles play in problems involving parallel lines and transversals?
8. Can the concept of co-interior (consecutive) angles be used to determine parallelism? If so, how?

Tip:

When working with parallel lines and a transversal, always check for corresponding angles, alternate interior angles, and alternate exterior angles as they provide clear relationships to solve for unknown values.