Verified answer

[tex]\displaystyle\bf\\x^{3} -5x^{2} +9x-45=0\\\\(x^{3} -5x^{2} )+(9x-45)=0\\\\x^{2} \cdot(x-5)+9\cdot(x-5)=0\\\\(x-5)\cdot(x^{2} +9)=0\\\\x^{2} +9\neq 0\\\\x-5=0\\\\\boxed{x=5 }[/tex]