The period of a sinusoidal function is determined by the coefficient of (x) in the cosine or sine function. For the function (y = -3 \cos\left(\frac{2\pi}{5}x\right)), the coefficient of (x) is (\frac{2\pi}{5}). The period (P) is given by the formula (P = \frac{2\pi}{\text{coefficient of } x}). Therefore, the period of this sinusoid is (P = \frac{2\pi}{\frac{2\pi}{5}} = 5).
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