My sink connects with my 5 inch cast iron toilet drain in the basement. Figured the clog was either in the P trap or somewhere before the piping reaches the toilet drain. Snaked it a couple times and is still clogged. I'm pretty sure the snake made it to the 5 inch piping....some sludge on it. Just don't get why water is not draining at all
I have had great results with my high quality drum auger, as opposed to some of the inferior models available at big-box stores. The design of the tip helps the cable to move downward and so helps prevent inadvertent travel up a vent line. I have had the same unit for 16 years and cleared hundreds of clogs. Not a recommendation for a particular brand, but good quality tools work better.
Most of the time bathroom sinks clog closer to the drain itself. Hair tangles on the stopper and collects soap and tooth paste then a bit more hair and it is plugged. Lust last week I pulled my stopper a small nut on the back side that has a lever connecting to the rod that you pull up / down , pull that nut slide the shaft out and some times the clump will fall out, if it is a drain stopper you press directly down on to stop the sink and then press again to open the top will usually unscrew and you may be able to pull the plug, worst case you may need to remove the pipe, in both above cases a nut tightens the assembly to the sink, remove this nut and push the pipe up I have had to do this to clean out plugs that were just below the basin but above the trap. If you need to remove the pipe it might need a new seal if not rubber and a little plumbers putty wrapped around the pipe at the bevel (top) will seal the sink when the nut is retightened. I believe this is where your plug is since you have snaked the main drain line.