\(16x^2\left(x-5\right)+5-x=0\)
\(\Leftrightarrow16x^2\left(x-5\right)-\left(x-5\right)=0\)
\(\Leftrightarrow\left(x-5\right)\left(16x^2-1\right)=0\)
\(\Leftrightarrow\left(x-5\right)\left[\left(4x\right)^2-1^2\right]=0\)
\(\Leftrightarrow\left(x-5\right)\left(4x-1\right)\left(4x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-5=0\\4x-1=0\\4x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=\dfrac{1}{4}\\x=-\dfrac{1}{4}\end{matrix}\right.\)
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