smc

We have $x^5\left(x+\frac{1}{x}\right)\left(1+\frac{2}{x}+\frac{3}{x^2}\right)=(x^6+x^4)\left(1+\frac{2}{x}+\frac{3}{x^2}\right)=x^6+\text{lower order terms}$, where we know that the $x^6$ will not get cancelled out by e.g. a $-x^6$ term since all the terms inside the brackets are positive. Thus the degree is $6$, which is choice $\boxed{6}$.