To find the ratio of chicken wings to sandwiches, we take the number of chicken wings (25) and the number of sandwiches (40) and express it as a fraction:
\[ \text{Ratio} = \frac{\text{Number of chicken wings}}{\text{Number of sandwiches}} = \frac{25}{40} \]
Next, we simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 25 and 40 is 5.
Now, we divide both 25 and 40 by 5:
\[ \frac{25 \div 5}{40 \div 5} = \frac{5}{8} \]
Therefore, the ratio of chicken wings to sandwiches in simplest terms is:
\[ \boxed{\frac{5}{8}} \]