To solve the equation
\[ \log_2(x-3) - \log_2(3) = 5, \]
we can use the properties of logarithms. Specifically, we can combine the two logarithms on the left side using the quotient rule:
\[ \log_2\left(\frac{x-3}{3}\right) = 5. \]
To eliminate the logarithm, we can exponentiate both sides with base 2:
\[ \frac{x-3}{3} = 2^5. \]
Calculating \(2^5\) gives us 32:
\[ \frac{x-3}{3} = 32. \]
Next, we can multiply both sides by 3 to get rid of the fraction:
\[ x-3 = 32 \cdot 3. \]
Calculating \(32 \cdot 3\) gives us 96:
\[ x - 3 = 96. \]
Now, add 3 to both sides:
\[ x = 96 + 3. \]
Thus,
\[ x = 99. \]
Finally, the solution is:
\[ \boxed{99}. \]