Since 5 is a factor of 10 and 15 (by guess and check with factors of 10 and seeing if they're factors of 15), we get 5(3x^2y^3+2xy^2z). Next, y^2 is in both - remember that when multiplying exponents, you add them up, so we end up with 5y^2(x^2y+2xz). Lastly, x (aka x^1) is in both, so we factor that out to end up with 5y^2x(xy+2z)
