You need to disconnect the batteries in series before charging. If you plug it in like this it will let the magic smoke out! You are still in series and will short.
Disconnect series, and charge two 5s batteries. OR get a 10s charger and charge at 10s voltage w/ split balance leads. ( I have the http://www.hobbypartz.com/75p-1220-charger.html - which does this). It’s meh. No real advanced settings like on iCharger (miss the IR measurement in particular). But does work for this.
Actually it is possible to do as you have illustrated because you are in effect isolating each battery with charge leads.
I have done this with my 5 x 2s in series 10s setup and it worked just fine.
Just use a hobby balance charger and charge each pack separately. DO NOT charge both packs together in parallel