What is the degree of this polynomial 15x^5z^2-7y

That polynomial is made up of 2 terms, and 7y, separated by a minus sign.  To find the degree of a polynomial you consider the term with the highest degree, no matter that the variables are different.  The degree on the first term is 5+2=7, whereas the degree on the second term is just 1.  Since the degree of a polynomial is equal to the degree of the term that is highest, our degree is 7.

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