Chọn phương án A.

\(\begin{align*}\displaystyle\int\limits_{\tfrac{1}{3}}^1\dfrac{x-5}{2x+2}\mathrm{\,d}x&=\dfrac{1}{2}\displaystyle\int\limits_{\tfrac{1}{3}}^1\dfrac{x-5}{x+1}\mathrm{\,d}x\\
&=\dfrac{1}{2}\displaystyle\int\limits_{\tfrac{1}{3}}^1\left(1-\dfrac{6}{x+1}\right)\mathrm{\,d}x\\
&=\dfrac{1}{2}\left(x-6\ln|x+1|\right)\bigg|_{\tfrac{1}{3}}^1\\
&=\dfrac{1}{3}-3\left(\ln2-\ln\dfrac{4}{3}\right)\\
&=\dfrac{1}{3}+3\ln\dfrac{2}{3}\\
&=\dfrac{1}{3}+\ln\dfrac{8}{27}.\end{align*}\)

Theo đó \(a=\dfrac{1}{3}\), \(b=\dfrac{8}{27}\)
\(\Rightarrow ab=\dfrac{1}{3}\cdot\dfrac{8}{27}=\dfrac{8}{81}\).