In the polynomial expansion of $(x+y)^5$, what is the coefficient of the $x^2y^3$ term?

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We can use the binomial theorem. The coefficient is:

$$\binom{5}{3} = {}_5C_3 = \frac{5!}{(5-3)!3!}$$ $$= \frac{5\cdot4\cdot3\cdot2}{2\cdot3\cdot2}$$ $$= \boxed{10}$$