Step 1 :Identify the highest power of the variable in the polynomial \(s(x)=5x^{2}+4x-12\). This is the degree of the polynomial.
Step 2 :The highest power of the variable x in the polynomial \(s(x)=5x^{2}+4x-12\) is 2. Therefore, the degree of the polynomial is \(\boxed{2}\).
Step 3 :Identify the coefficient of the term with the highest degree in the polynomial \(s(x)=5x^{2}+4x-12\). This is the leading coefficient of the polynomial.
Step 4 :The coefficient of the term with the highest degree (which is \(x^{2}\)) in the polynomial \(s(x)=5x^{2}+4x-12\) is 5. Therefore, the leading coefficient of the polynomial is \(\boxed{5}\).