\(5^{x+4}-3.5^{x+3}=2.5^{11}\)
\(\Leftrightarrow5^{x+3+1}-3.5^{x+3}=2.5^{11}\)
\(\Leftrightarrow5^{x+3}.5-3.5^{x+3}=2.5^{11}\)
\(\Leftrightarrow5^{x+3}.\left(5-3\right)=5^{11}.2\)
\(\Leftrightarrow5^{x+3}.2=5^{11}.2\)
\(\Leftrightarrow5^{x+3}=5^{11}\)
\(\Leftrightarrow x+3=11\)
\(\Leftrightarrow x=8\)
Vậy \(x=8\)