Problem Statement: Calculate the displacement at an angle of 60 degrees to the x-axis that has an x-component of 5m.

Explanation:
To solve this problem, we will use the concept of vector components.

Step 1: Draw a diagram of the displacement vector with respect to the x and y-axis.

Step 2: Identify the angle of the displacement vector with respect to the x-axis. In this case, the angle is given as 60 degrees.

Step 3: Calculate the x-component of the displacement vector. The x-component is given as 5m.

Step 4: Use trigonometry to calculate the y-component of the displacement vector.

Step 5: Use the Pythagorean theorem to calculate the magnitude of the displacement vector.

Step 6: Write the final answer in vector notation.

Calculations:
- The x-component of the displacement vector = 5m
- The angle of the displacement vector with respect to the x-axis = 60 degrees
- Using trigonometry, the y-component of the displacement vector can be calculated as y = x*tan(θ) = 5m*tan(60) = 8.66m
- Using the Pythagorean theorem, the magnitude of the displacement vector can be calculated as d = sqrt(x^2 + y^2) = sqrt(5^2 + 8.66^2) = 10.2m
- The final answer in vector notation is: d = 10.2m at an angle of 60 degrees to the x-axis.

Conclusion:
The displacement at an angle of 60 degrees to the x-axis that has an x-component of 5m is 10.2m at an angle of 60 degrees to the x-axis.