What is the amplitude of the sinusoid given by y=-5sin (7x) ?

5.

When we look at the amplitude of a sine wave, we want to know how high its peaks and how low its valleys are. The graph of y = sin (x) rises to a high of 1 at its peaks and a low of - 1 at its valleys, so its amplitude is 1. Multiplying the function by 5 makes its peaks and valleys 5 times higher and lower - y = 5sin (x) has an amplitude of 5 for that reason.

Flipping the 5 to a - 5 doesn't change the amplitude; it simply swaps the peaks for the valleys, so our amplitude will still be 5.