\(\dfrac{x-1}{x+5}=\dfrac{x-3}{x+4}\)
\(\Rightarrow\left(x-1\right)\left(x+4\right)=\left(x-3\right)\left(x+5\right)\)
\(\Rightarrow x\left(x+4\right)-\left(x+4\right)=x\left(x+5\right)-3\left(x+5\right)\)
\(\Rightarrow\left(x^2+4x-x\right)-4=\left(x^2+5x-3x\right)-15\)
\(\Rightarrow x^2+3x=x^2+2x-11\)
\(\Rightarrow x=-11\)