B737 Captain reported failure of the left pack and loss of pressurization during cruise descent. Flight crew performed rapid descent and continued flight.

Narrative

On flight from ZZZ to ZZZ1; on Initial descent from FL320 to FL270 we were given the clearance to descent to FL270 followed by a second clearance to turn 15 degrees to the left. As we were approaching FL270 a sudden a simultaneous illumination of the red Cabin Altitude light and Horn sounded. My reaction was to execute the cabin rapid depressurization memory items followed by the reading of our QRH. The accomplishment of the immediate memory items by the Captain followed by the QRH read by First Officer in concurrence with the Captain. For us our priority was to aviate; navigate and then communicate. Because of the recognition of loss of pressurization and the constant sounding of the Horn and the attempt to control the cabin pressure by closing the outflow valve. We requested a lower altitude; however; due to the loud noises in the cabin and the use of oxygen mask; although we as crew had already established communications. The ATC Controller couldn't hear our request for lower altitude. Which led her to [request priority handling] for us. To which we agreed and at the same time we continued our descend to 10;000FT as per the QRH. Upon reaching 10;000FT; the horn stopped sounding and the FO removed his oxygen mask first and everything was under control. Cause: The sudden Lost of the Left Pack.Suggestions: The good monitoring and maintenance of the aircraft's pressurization system.