How to properly handle power / gnd pads on power / gnd planes

It looks like you need to set the thermal relief for the power plane to something greater than zero. Your pin 5 will still be connected to the power plane (as it should be). You can then put the bypass cap near pin 5 and make the connection to ground (the +3.3V pin of the cap will attach to the power plane automatically, just like pin 5).