Bad background noise in audio capture
I had a look at your audio file.

You have two major noises going on.

One is powerline hum.  You have a 60 Hz hum, with a lot of harmonics.

This is the spectrum:



The biggest peak is at 60 Hz, the next highest one is at 180Hz.

The other thing you've got going on is a high pitched squeal at around 10kHz, that seems to be mixed with some other trash:



The hum could get in a couple of ways:


You have what is known as a "ground loop."  Ground in individual outlets in your home aren't necessarily all at the same potential.  If you have your ALC5640 codec powered by a a powersupply in one outlet, and it is connected via USB to your PC on another outlet, then you can get a lot hum.
Unshielded wire and some "noisy" power using device near your circuit.


The squeal could come from a few places as well.


The powersupply for the ALC5640.  A switching powersupply could make that kind of racket.
Conduction from your PC or what ever other device you have it connected to,
The ALC5640 circuit itself.  Digital ICs (even ones intended for use around audio) produce a lot of trash.


You'll need to investigate the possible sources yourself, and eliminate each until you find the culprit.

Better decoupling may help with the squeal, or a better powersupply.

For the hum, try powering your circuit from batteries, or a known good (quiet) powersupply.