What does the schematic for a 5 to 1 multiplexer look like
For a 5-to-1 mux you must have (at least) 3 select inputs since 2 select inputs can only select from 4 data inputs. But with 3 select inputs there are 8 patterns, which is why you usualy have a 8-to-1 mux. But not every select pattern needs to have a unique choice. Consider a setup where select inputs 000-011 select data inputs A1-A4 and 100-111 always selects data input A5.

You can build such a 5-to-1 mux easily in two ways:

1) Take a 4-to-1 mux, connect A1-A4 and S0-S1 to it. Take the output of the 4-to-1 mux and connect it to one input of a 2-to-1 mux. Connect A5 and S2 to the remaining pins. Now you have a 5-to-1 mux.

2) Take a 8-to-1 mux and connect the A5 input to A6-A8 too.

Both ways can be optimized to use fewer gates if you aren't using premade ICs. Or you can design a 5-to-1 mux from scratch. Write out the truth table, solve the Karnaugh diagrams and optimize the logic function and so on.