\({3^{{{\log }_9}\left( {5x — 5} \right)}} = 5\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,{3^{{{\log }_9}\left( {5x — 5} \right)}} = {3^{{{\log }_3}5}}\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,{\log _9}\left( {5x — 5} \right) = {\log _3}5\,\,\,\,\,\, \Leftrightarrow \)
\( \Leftrightarrow \,\,\,\,\,\,{\log _9}\left( {5x — 5} \right) = {\log _{{3^2}}}{5^2}\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,{\log _9}\left( {5x — 5} \right) = {\log _9}25\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,5x — 5 = 25\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,x = 6.\)
Ответ: 6.