Showing that deciding whether a given TM accepts a word of length 5 is undecidable
Suppose that $M$ halts on input $w$ and consider the behaviour of $M'$ when it is given input&nbsp;$w'\!$. $M'$ first deletes its input $w'$ and replaces it with $w$, which means that the behaviour of $M'$ doesn't depend on what input it actually receives. Then, $M'$ simulates $M$ on input&nbsp;$w$. So, if $M$ halts on $w$, $M'$ halts for every input, becaues $M'$ ignores its input and just pretends to be $M$ running with input&nbsp;$w$. Likewise, if $M$ does not halt on&nbsp;$w$, $M'$ doesn't halt for any input.