Identify each term in the polynomial: \(-3x^{2}\), \(-5x^{2}y^{2}\), and \(y^{3}\).
For each term, find the degree by adding the exponents of all variables in that term. For example, in \(-3x^{2}\), the degree is \(2\) because the exponent of \(x\) is \(2\).
Calculate the degree of the second term \(-5x^{2}y^{2}\) by adding the exponents: \(2\) (from \(x^{2}\)) plus \(2\) (from \(y^{2}\)), which gives a total degree of \(4\).
Calculate the degree of the third term \(y^{3}\), which is simply \(3\) because the exponent of \(y\) is \(3\).
The degree of the polynomial is the highest degree among all its terms, so compare the degrees \(2\), \(4\), and \(3\) to determine the polynomial's degree.