Evaluate and simplify \(\frac{5}{{13}} \times \frac{{221}}{{220}}\).

\[\begin{align}
 \frac{5}{{13}} \times \frac{{221}}{{220}} &= \frac{{{\color{red}\cancel {\color{#444}{5}}}}}{{{\color{red}\cancel {\color{#444}{13}}}}} \times \frac{{{\color{red}\cancel {\color{#444} {13}}} \times 17}}{{2 \times 2 \times {\color{red}\cancel {\color{#444}{5}}} \times 11}} \\
  &= \frac{{17}}{{2 \times 2 \times 11}} \\
  &= \frac{{17}}{{44}} \\
 \end{align}\]