To solve the equation \( \log_2(x - 3) - \log_2(3) = 5 \), we can use the properties of logarithms. Specifically, we will use the property that \( \log_a(b) - \log_a(c) = \log_a\left(\frac{b}{c}\right) \).
Using this property, we can rewrite the equation as:
\[ \log_2\left(\frac{x - 3}{3}\right) = 5 \]
Now, to eliminate the logarithm, we will exponentiate both sides, using the fact that if \( \log_a(b) = c \), then \( b = a^c \):
\[ \frac{x - 3}{3} = 2^5 \]
Calculating \( 2^5 \):
\[ 2^5 = 32 \]
Thus, we have:
\[ \frac{x - 3}{3} = 32 \]
Now we can solve for \( x \) by multiplying both sides by 3:
\[ x - 3 = 96 \]
Next, we add 3 to both sides:
\[ x = 96 + 3 = 99 \]
So the solution is:
\[ \boxed{99} \]