To find the maximum number of guests Gabe can invite for his retirement party within his budget of $50, let's first determine the cost per guest.
Given that the retirement party costs $25 for 5 guests, we can find the cost per guest as follows:
\[ \text{Cost per guest} = \frac{\text{Total cost}}{\text{Number of guests}} = \frac{25}{5} = 5 \]
So, the cost per guest is $5.
Now, let's determine how many guests he can invite with a total budget of $50. We can set up the equation based on the cost per guest:
\[ \text{Total cost} = \text{Cost per guest} \times \text{Number of guests} \]
Substituting the values we have:
\[ 50 = 5 \times \text{Number of guests} \]
To find the number of guests, we divide both sides by 5:
\[ \text{Number of guests} = \frac{50}{5} = 10 \]
Thus, the maximum number of guests Gabe can invite is:
\[ \boxed{10} \]