A soft reset would be more like the normal powering down function on the iPhone...the equivalent "battery pull" would be a hard reset, or holding the home and power button down until the phone shuts down.
To the OP, if you're not jailbroken, the chances that one of the apps is causing laggy performance in general on your iPhone is pretty low (though not impossible). The best way to figure that out would be to go back to when you remember the phone starting to have performance issues and then deleting any apps you DL'ed around that time (and reloading them if they are important to you), it is possible that you had a bad sync if you recently updated your firmware on it, and it's also possible that you have a hardware issue and it needs to be replaced.
Personally, i wouldn't take the chance in any of these situations...your iPhone 5 is still under full warranty, which means you'll get a brand spanking new one if you go in and let them know what's going on (and even easier if you can replicate the issue IN store). Get a replacement, that way in the future even if you get it to start performing normal now, you don't have this same issue creep back up after the warranty is over.