To find the work done by a force, we use the formula:

Work = Force * Displacement * cos(theta)

where:
- Force is the magnitude of the force
- Displacement is the displacement vector
- theta is the angle between the force vector and the displacement vector.

In this problem, we are given the following information:
- Force magnitude: 5 units
- Displacement vector: 2i - 2j + k
- Initial point: (1, 2, 3)
- Final point: (5, 3, 7)

1. Calculating the Displacement Vector:
To find the displacement vector, we subtract the initial point from the final point:

Displacement = (5 - 1)i + (3 - 2)j + (7 - 3)k
= 4i + 1j + 4k

2. Calculating the Magnitude of the Displacement Vector:
The magnitude of the displacement vector is given by the formula:

Magnitude = sqrt((x^2) + (y^2) + (z^2))

where x, y, and z are the components of the displacement vector. Plugging in the values:

Magnitude = sqrt((4^2) + (1^2) + (4^2))
= sqrt(16 + 1 + 16)
= sqrt(33)

3. Calculating the Angle between the Force and Displacement Vectors:
To find the angle between the force and displacement vectors, we can use the dot product formula:

Dot Product = |A| |B| cos(theta)

where A and B are the vectors and theta is the angle between them. Rearranging the formula:

cos(theta) = Dot Product / (|A| |B|)

The dot product of the force and displacement vectors can be found by multiplying their corresponding components and adding them up:

Dot Product = (2 * 4) + (-2 * 1) + (0 * 4)
= 8 - 2 + 0
= 6

Substituting the values into the equation for cos(theta):

cos(theta) = 6 / (5 * sqrt(33))

4. Calculating the Work Done:
Finally, we can calculate the work done by substituting the given values into the work formula:

Work = Force * Displacement * cos(theta)
= 5 * sqrt(33) * (4i + 1j + 4k) * (6 / (5 * sqrt(33)))
= 5 * (4i + 1j + 4k) * (6 / 5)
= 5 * 6
= 30

Therefore, the work done is 30 units. However, none of the given options match this answer. Please double-check the provided answer choices.