**Proof that a Regular Polygon has 5 Sides**

To prove that a regular polygon has 5 sides, we will use the given information that the exterior angle is 2/3 of the interior angle. Let's proceed with the proof step by step:

**Step 1: Define the interior and exterior angles**
- Interior angle: The angle formed inside the polygon between two adjacent sides.
- Exterior angle: The angle formed outside the polygon by extending one side of the polygon.

**Step 2: Express the relationship between interior and exterior angles**
Let's assume the measure of the interior angle of the regular polygon is x degrees. Since the exterior angle is 2/3 of the interior angle, we can express it as (2/3)x degrees.

**Step 3: Consider the sum of exterior angles**
In a polygon, the sum of all exterior angles is always 360 degrees. Therefore, we can write the equation:

(2/3)x + (2/3)x + (2/3)x + (2/3)x + (2/3)x = 360

Simplifying this equation, we get:

(10/3)x = 360

**Step 4: Solve for x**
To find the value of x, we can multiply both sides of the equation by 3/10:

x = (3/10) * 360
x = 108

Therefore, the measure of the interior angle is 108 degrees.

**Step 5: Determine the number of sides**
In a regular polygon, the sum of all interior angles is given by the equation:

Sum of interior angles = (n - 2) * 180

where n is the number of sides of the polygon.

For our regular polygon, we can substitute the values:

(n - 2) * 180 = 108

Simplifying this equation, we get:

n - 2 = 108 / 180
n - 2 = 0.6

Adding 2 to both sides of the equation, we get:

n = 2.6

Since the number of sides must be a whole number, the regular polygon must have 5 sides.

**Conclusion**
By using the given information that the exterior angle is 2/3 of the interior angle, we have successfully proved that a regular polygon with this condition must have 5 sides.