Remember that according to the binomial theorem, the expression that gives the expansion of a binomial (a+b) raised to the nth power is:
[tex](a+b)^n={\displaystyle \sum_{k=0}^n{C(n,k)a^{n-k}b^k}}[/tex]The first term can be obtained plugging in k=0, the second term by plugging in k=1 and the third term by plugging in k=2. Then, the third term of (x+2)^5 is given by the expression that results after setting n=5, k=2, a=x and b=2:
[tex]\begin{gathered} C(n,k)a^{n-k}b^k \\ \Rightarrow \\ C\left(5,2\right)x^{5-2}2^2=C\left(5,2\right)x^32^2 \end{gathered}[/tex]Therefore, the correct choice is:
[tex]C(5,2)x^32^2[/tex]