${\left( \frac{ 5 }{ 3 } \right)}^{x-1}={\left( \frac{ 5 }{ 3 } \right)}^{-4x+14}$
Since the bases are the same, set the exponents equal$x-1=-4x+14$
Move the variable to the left-hand side and change its sign$x-1+4x=14$
Move the constant to the right-hand side and change its sign$x+4x=14+1$
Collect like terms$5x=14+1$
Add the numbers$5x=15$
Divide both sides of the equation by $5$$x=3$