Degree of a polynomial is the highest power of the variable in the polynomial.

(i) 5x^{3} + 4x^{2 }+ 7x

This is a polynomial in variable x and the highest power of variable x is 3. Therefore, the degree of this polynomial is 3.

(ii) 4 - y^{2}

This is a polynomial in variable y and the highest power of variable y is 2. Therefore, the degree of this polynomial is 2.