For domain of given function

Denominator \(\displaystyle\ne{0}\)

\(\displaystyle\therefore{\left({x}-{3}\right)}{\left({x}-{5}\right)}\ne{0}\)

\(\therefore x \ne 3, x \ne 5\)

\(\displaystyle\therefore{x}\in{\left(-\infty,{3}\right)}\cup{\left({3},{5}\right)}\cup{\left({5},\infty\right)}\)

or domain is all real numbers except 3 and 5.