This question is from Exercise 7.1, Question 2. The student needs to apply the binomial theorem for $(a - b)^n$ expansion.

Using the formula:

$$(a - b)^n = {}^{n}C_0 \cdot a^n - {}^{n}C_1 \cdot a^{n-1} \cdot b + {}^{n}C_2 \cdot a^{n-2} \cdot b^2 - \cdots + (-1)^n \cdot {}^{n}C_n \cdot b^n$$

we substitute $a = \frac{2}{x}$, $b = \frac{x}{2}$, and $n = 5$.

The binomial coefficients for $n = 5$ are:

$${}^{5}C_0 = 1, \quad {}^{5}C_1 = 5, \quad {}^{5}C_2 = 10, \quad {}^{5}C_3 = 10, \quad {}^{5}C_4 = 5, \quad {}^{5}C_5 = 1$$

Each term requires careful simplification of powers of fractions.