Don't think for a minute that running clubs are filled with athletes. Just like tennis clubs aren't filled with Andy Murray wannabes.
There will be plenty of people there who are the same, better or worse than you at running.... and they don't leave people behind.
If you ask me, they are a perfect place for someone who's not so good at meeting people. Because you can choose to blend in a bit if you like - and it isn't at all awkward if you don't chat too much... but then there are plenty of opportunities for small talk... or longer conversations whilst you run, if you feel like it. There's nothing forced about it... over a period of weeks you start to fit in and slowly get to know quite a few people.
On another subject... if you've gone from zero to 5/6 miles every other day in the space of a month... just be careful. Your heart and lungs can adapt quickly... and for you, that must be happening. But your leg muscles, tendons, bones... they also all need to adapt to the repetitive stresses involved in running, and that normally takes longer. They say that the prime time for new runners to pick up an injury is after 1-3 months. The 'damage' is cumulative and often manifests itself at this point unless you're giving enough time for your body to repair itself (of course, this natural cycle of micro-damage and repair is all part of the natural process for your body to adapt and improve).
So... just be patient. You might be lucky, but certainly watch out for niggles in this next couple of months, and ease back on the miles a little if appropriate.