Panic attacks can last a lot longer, mine tend to phase in and out of intensity for 30 mins or so... once I've had one I tend to have more cause I'm paniced about being paniced!

The thing with panic attacks is they are your bodies natural response to a dangerous situation. The rush of 'panic' you feel is your body jacking you full of some serious drugs in preparation of fight or flight...some retard pain, some increase reaction (this is what bangs your heart rate through the roof) speed and some are muscle relaxants so that if you have to act fast without warming up you wont pull a muscle, casue it'd be a really bad time to do it. This is also why people pee and pooh themselves from fear...its all about preparation for the fight or flight.
Whats gone wrong is not the panic attack but your brain, which for some reason has logged certain stimuli as 'dangerous' that really isnt, and when ever you are exposed to these stimuli, you get the same physiological response as if a black bear was running you down!
It has become such a problem because these days as stress is rarely related to physical danger, if your in physical danger you feel the fear, run away or fight then have a right good laugh about it with your mates. This is cause the strenuous activity burns up the 'panic' chemicals and then floods you with feel good chemicals and all is fine. But when the panic is inappropriate, ie when your not in danger they dont get burned up and you dont get the 'high' that chills you out after. You get to just stew in the crappy chemical cocktail... This is why strenuous activity is of such benefit. I fight mma, cause the training is hard...but when I was young I did triathlon...anything sufficiently hard will help.
An important thing to do is to figure out what sets you off. If its not obvious take a notebook and write down when where you are and what your doing when it happens. Your mind will try to play all sorts of tricks on you to convince you you are in danger, one of the worst is it will try to associate the attacks with certain places. I have terrible trouble on one train line, not all trains, just this specific line between two specific stops. When you find what your triggers are, it helps. Dont avoid the place, but understand that some days you feel stronger than others and that on weak days it can be best to avoid your triggers, and on strong days confront them.
As people have said before, one of the best ways to deal with them in the short term is distraction, I usually phone my bro (who also gets them) and chat about stuff, anything like fish or whatever. Or i'll phone my missus and chat. Music also helps me if I blast it!!! If I'm on my own I find moving helps, just keep walking/running ar if I'm confined, I drop and go through a routine of pressups, situps, squats ect...that gets some looks on the train, but they are use to me now!
They almost always stem from some stressful situation somewhere else in your life, and in order to get them to stop you need to figure out what that is and try and lower the stress levels...a good period of chill is the best cure...I prescribe lots of time watching your fish float about!!!
ps avoid coffee, coke, alcohol any other stimulants, they dont usually help...