I have a double sink in my kitchen. When the 1st sink is plugged and is full with water and I begin to use the 2nd sink the water starts to back up. When I pull the plug on the 1st. Sink a large air bubble surfaces and the water starts to flow better in the 2nd sink. Both sinks join into one pipe under the sink... and the pipe extends over about 5 feet and then drops down vertically about 8ft. I have no idea what is going on... what could this be... I recently had the downstairs pipe snaked out in which this sink flows into..

Liquid Plummer Gel
Does wonders :D

You have a partial blockage in the horizontal line in the wall. Take the trap apart and send a snake up into the wall. You will run into a elbo about 8 inches in. Work your way around it aqnd you only have 5 more feet to go. Flush with hot water. Good luck, Tom