Line A is both perpendicular to line B and parallel to line C. If the slope of C is 14/5, which of the following is the slope of B?

If line A is both perpendicular to line B and parallel to line C, then line A must be perpendicular to line B and have the same slope as line C. Therefore, the slope of line B must be $\boxed{-\frac{5}{14}}$.