I had my speedo replaced under warranty 500 kms ago and the hesitation problem in 5th gear has not reappeared.
So there are well-documented problems with the speedo on the 350 classic. Tiger Ness had the faceplate peel away and jam the needle, but mostly I think people (like me) have had the needle simply fail to return to zero. Upon restarting, any acceleration is added to the rest position. This can usually be rectified by switching the ignition on, waiting for the sweep to finish, turning off and then repeat however many times it takes to return to zero (took me eight tries). Bear with me.
Now the abs, the speedo and the ecu pick up their signal from the front abs sensor. I suspect the funky speedo may be interfering with the abs signal, confusing the ecu which then "thinks" you must be exceeding the maximum permissible top speed and then cuts the fuel injection way back to correct your naughty behavior. (Now, besides the fact that had I known, no matter how pretty, I would never have purchased a bike with an effing speed limiter built-in to appease the effing EU nanny state....)
In my past correspondence with Enfield, they referred to the 5th gear hesitation as a misfiring. I don't think so. In my experience, misfiring is followed by backfiring as excess unburnt fuel in the exhaust is burnt off, once proper ignition returns. There is no evidence of that.
At any rate, the speedo has been replaced and at least 500kms in and the hesitation in 5th gear has not returned.