The given triangle has the following details:

• The angle $62^\circ$,
• The side adjacent to the angle is 5,
• The missing side $x$ is opposite the angle.

We can use the tangent trigonometric function: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}.$ Substituting the given values: $\tan(62^\circ) = \frac{x}{5}.$

Rearranging for $x$: $x = 5 \cdot \tan(62^\circ).$

Now let's calculate $x$:

1. Find $\tan(62^\circ)$: Using a calculator, $\tan(62^\circ) \approx 1.8807$.
2. Multiply:
   $x = 5 \cdot 1.8807 \approx 9.40.$

It seems the options given in the problem do not include the correct result, so let me double-check the context and calculations.

Would you like a detailed reanalysis or further clarification? Here are related questions:

1. What is the difference between tangent and sine functions in trigonometry?
2. How can calculators ensure precision for trigonometric calculations?
3. What are common applications of trigonometry in physics and engineering?
4. How does the accuracy of angle measurements affect the result?
5. Why do trigonometric problems often include rounding instructions?

Tip: Always double-check the mode of your calculator (degrees vs. radians) when solving trigonometric equations!