### Step-by-Step Solution:
1. Identify the Given Values:
- The edge length of the square base of the pyramid is \( 5 \, \text{cm} \).
- The height of the pyramid is \( 7 \, \text{cm} \).
2. Calculate the Area of the Base:
Since the base is a square, the area \( A \) of the base can be calculated using the formula for the area of a square:
[tex]\[
\text{Area of the base} = \text{edge length}^2 = 5 \, \text{cm} \times 5 \, \text{cm} = 25 \, \text{cm}^2
\][/tex]
3. Use the Formula for the Volume of a Pyramid:
The volume \( V \) of a pyramid is given by the formula:
[tex]\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\][/tex]
Substituting the values we calculated and were given:
[tex]\[
V = \frac{1}{3} \times 25 \, \text{cm}^2 \times 7 \, \text{cm}
\][/tex]
4. Perform the Multiplications:
First, multiply the base area by the height:
[tex]\[
25 \, \text{cm}^2 \times 7 \, \text{cm} = 175 \, \text{cm}^3
\][/tex]
5. Divide by 3:
Now, divide the product by 3 to find the volume:
[tex]\[
V = \frac{175 \, \text{cm}^3}{3} = 58.33333333333333 \, \text{cm}^3
\][/tex]
6. Express the Volume as a Mixed Number:
To express the volume as a mixed number:
[tex]\[
58.33333333333333 \approx 58 \frac{1}{3} \, \text{cm}^3
\][/tex]
### Conclusion:
The volume of the pyramid, given a square base with edge length \( 5 \, \text{cm} \) and a height of \( 7 \, \text{cm} \), is:
[tex]\[
58 \frac{1}{3} \, \text{cm}^3
\][/tex]
### Answer:
[tex]\[
\boxed{58 \frac{1}{3} \, \text{cm}^3}
\][/tex]
