Maybe you should have asked the person who told you to go to a higher (bigger?) gear. 

Since I wasn't there, I'm guessing that you were in a gear that was too low based on your information that you were at 90rpm but not breathing hard.  If you had geared up and reduced the rpm, but pushed the gear a little harder, you might have been able to keep up.  Keep in mind I'm talking about subtle gear changes, not so that you would cause injury.  

Well, arrange to ride with them again but rest your legs the day before.  And try gearing up just a bit and decreasing the rpm's just a little bit.  90 rpm seems a little fast to me.  I generally ride in upper 70's to lower 80's depending on lots of variables.  Pick out someone you think you can hang with and try to match their gear selection and cadence.  You have a bike and it's summer time, why are you taking spinning classes?  Also add some recovery rides the day following a hard ride.  Your legs are still sore?  Are you doing enough stretching?  Skip the spinning and take a yoga or pilates class.  Nothing wrong with being in the back of the pack, especially at 59.

Push yourself with the group ride.  You get better by riding with better riders.  It would seem you have hit a plateau, time to mix things up.  So no spinning class, group ride instead for the next 5 weeks, then check back in. 

The advice you got about cranking out a bigger gear to keep up is flat out incorrect.  Keeping a consistent cadence of between 85-120 is proven to provide better efficiency.  Spinning out at a faster cadence requires you to use less power overall for the same amount of speed, and keeping a high cadence will keep you safer in a group.  Churning out a huge gear will make it hard to keep a consistent speed, and that can be a problem in a group ride.  Just to put a gold star on my advice, Lance increased his cadence from 80-90 to an average of 115 early in his career to accieve higher efficiency.  Keep up the high cadence man, its just all around better for your body...it also helps move lactic acid, keeping you fresher.

Oma, sorry to see that you felt attacked by my response.  I in no way was trying to insult you.  In fact, I was not even responding to what you were saying...I was upset that someone during a ride gave him general advice that was, at the very least, not specific enough to help him.  Please understand what I was trying to suggest, even if I did a horrible job of it.  There have been numerous studies on this subject and the underlying agreement is that in general a cadence between ~80-115 is most EFFICIENT.  The amount of energy spent during cycling at a cadence in that range is less than if you are going at a lower cadence.  In general, what you will find, is that a lower cadence pushes the muscular system harder than the cardio vascular system; spinning at a higher cadence uses the cardio system more.  A person can use there cardio system at a high rate longer and more efficiently than they can using there TII muscles with a lower O2 consumption.  There is a bit of training needed to achieve a high cadence, you will have a higher level of cardio strength with that kind of training.  That being said...there are some people with unusual muscle compositions that may push them into being more efficient with a lower cadence...but in general, the majority of people can be more efficient by pushing their cadence up into the aforementioned range.