In the usual (a+b)ⁿ binomial expansion the third term will be
[tex]{n \choose 2} a^{n-2}b^2[/tex]
Note we used k=2 because the first term is k=0.
We have a=1/x, b=x^log x, n=5
5 choose 2 is (5×4)/2=10, n-2=3, so we end up with a third term of
[tex]\displaystyle {5 \choose 2} \left(\dfrac 1 x\right)^{5-2}\left(x^{log_{10} x}\right)^2 = \dfrac{10 \,x^{2 log_{10} x}}{x^3} = 10x^{-3 + 2 \log_{10}x}[/tex]
