I always thought electricity was some weird stuff. I am thinking maybe someone expected those five volt power supplies to be additive like with batteries. If we put two batteries negative to positive we get double the volts--no problems.
Guess power supplies don't work that way. lol
When covering the part of physical science dealing with electricity, I explain if you can understand water flow thru a pipe, you can understand electricity thru a wire. The power supplies could be used in exactly the way you claim if they don't share a common ground. Basically, you could hook the -5v output of one supply to ground and the ground (positive side) of that supply to the ground (negative side) of the +5v supply. You would then have your 10 v potential. In the situation I had, their grounds were already connected to the circuit board. Many semiconductor components are very polarity sensitive and will be "blown" almost instantly if the polarity is reversed.
On my wheel chair I have two twelve volt batteries which when put in series give me 24volts to run my DC motors on my electric wheel chair. I am thinking of getting another set of two and putting them in parallel and that will increase amp rating from 55 to 110 which will increase my range before needing to recharge.
I would strongly recommend hooking those batteries in series because you might well fry some of your components with the extra voltage. Now, if you don't have any voltage sensitive components and would like your chair to accelerate like a dragster, it might be fun. Back when slot cars were popular, I went to a place that had a scale 1/4 mile "dragstrip." My car had a 1.5 volt motor and the track provided 12v. The car ran the "quarter mile" in a little under two seconds with a scale speed of 700mph. I'd love to take a car like that to the drag strip.
Your idea of hooking the batteries in parallel is exactly right... it will increase the total power available and extend your range considerably... but probably a little less than double for other reasons.
Using the water in a pipe analogy.... volts are electric potential energy. Think of them as pressure. If I double the pressure in a hose, I can get a lot more water thru it in the same amount of time... so water out of the hose will travel much farther. On the other hand, amps are more like the total amount of water in the pipe. The more gallons you have, the longer it takes to empty the tank.