The piano string should be loosened.
Work Step by Step
The beat frequency of 3 Hz tells us that the piano string frequency is either 3 hertz above or 3 hertz below the tuning fork's frequency, but we don't yet know which. When the string is slightly tightened (which raises its natural frequency) the even higher beat frequency of 5 Hz means the piano tuner is moving the wrong way. The piano string's frequency must have started out 3 Hz above that of the tuning fork, and now it is 5 Hz above. The string should be loosened slightly until no beats are heard, at which point the string's frequency matches the tuning fork's frequency.