Construct triangle ABC, a = 5 cm, the median c is equal to 5 cm.

Solution:
1. Given:
- Side a = 5 \, \text{cm}
- Median to side c = 5 \, \text{cm}

2. Using properties of median:
- The median of a triangle divides it into two smaller triangles of equal area. Also, the median divides the opposite side into two equal segments.

3. Applying Apollonius's theorem, which relates sides of a triangle to the medians as follows:
b^2 + c^2 = 2m_c^2 + \frac{a^2}{2}
where m_c is the median to side c.

4. Substitute the given values:
b^2 + c^2 = 2(5^2) + \frac{5^2}{2}
b^2 + c^2 = 2(25) + \frac{25}{2}
b^2 + c^2 = 50 + 12.5
b^2 + c^2 = 62.5

5. Analyze feasibility:
- With side a = 5 \, \text{cm} and using b^2 + c^2 = 62.5, it follows that any feasible values of b and c must satisfy this equality, making sure triangle inequalities hold.

6. Generalization:
- Exact measurement of b and c would depend on specific triangle configuration, possibly producing different triangles.

Thus, potentially angles can vary, but the side relationships and median constraints must be maintained.