Cannot understand reductions from the halting problem and its complement
The machine $M'$ ignores its input, and just simulates $M$ running on $x$. Hence:

If $M$ halts on $x$ then $M'$ halts on all inputs.
If $M$ doesn't halt on $x$ then $M'$ doesn't halt on any input.

The notation $\tau(\langle M,x \rangle) = M'$ is the definition of a reduction $\tau$ from $\overline{HP}$ to $L_5$. The input to the reduction is an instance of the halting problem, which is a pair consisting of a Turing machine $M$ and an output $x$, and the output is the Turing machine $M'$ described above.