- x^3y^5/3
………………………………………

you're absolutely correct, it's a polynomial, well, it has only one term, recall that each term is separated by either "-" or "+", so we only have one term here, that makes it a monomial. Now, about the degree, for the degree of a polynomial, we look at each term, and add its variable's exponents, let's do that in this one.
[tex]-\cfrac{x^3y^5}{3}\implies -\cfrac{1}{3}x^3 y^5\impliedby degree~of~^{3+5},~na mely~\text{\LARGE 8}[/tex]