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To solve for \( V_5 \) using Kirchhoff's Voltage Law (KVL), we need to apply KVL around a loop in the circuit. According to KVL, the sum of the voltages around any closed loop is equal to zero. We will solve this by applying KVL to both the clockwise and counterclockwise loops.

### Clockwise Loop:
For the clockwise loop, sum all the voltages around the loop:

\[
V_1 + V_2 + V_3 + V_4 + V_5 = 0
\]

Substituting the given values:
- \( V_1 = 8.7 \, \text{V} \)
- \( V_2 = 14.6 \, \text{V} \)
- \( V_3 = 21.8 \, \text{V} \)
- \( V_4 = 20 \, \text{V} \)

The equation becomes:

\[
8.7 + 14.6 + 21.8 + 20 + V_5 = 0
\]

Solving for \( V_5 \):

\[
V_5 = -(8.7 + 14.6 + 21.8 + 20)
\]
\[
V_5 = -65.1 \, \text{V}
\]

Thus, the voltage \( V_5 \) is \( \boxed{-65.1 \, \text{V}} \).

Would you like further details or explanations? Here are some related questions you might consider:

1. What is Kirchhoff's Voltage Law and how is it applied in electrical circuits?
2. How can KVL be used in more complex circuits with multiple loops?
3. Can we solve the same problem using the counterclockwise loop? Would the answer be different?
4. What would happen if one of the voltage values in the circuit was unknown? How could we determine it using KVL?
5. How is KVL related to energy conservation in electrical circuits?

**Tip:** Always ensure that the polarities of the voltages are properly considered when applying Kirchhoff’s Voltage Law, as this is crucial for obtaining correct results.

Learn how to solve for the unknown voltage V5 in an electric circuit using Kirchhoff's Voltage Law (KVL). Detailed step-by-step solution includes the formula V1 + V2 + V3 + V4 + V5 = 0 and the application of KVL in electrical circuits. Suitable for Grades 10-12.

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