$5^{\log_{25}{(4x-7)}}=11$ 

$5^{\frac{1}{2}\log_{5}{(4x-7)}}=11$ 

$5^{\log_{5}{(4x-7)^{\frac{1}{2}}}}=11$ 

$5^{\log_{5}{\sqrt {4x-7}}} = 11$ 

$\sqrt {4x-7} = 11$ 

$4x-7 = 11^2$ 

$4x- 7 = 121$ 

$4x = 128$ 

$x = 32$ 

Ответ: 32