I would try the 5 degree increase at the start of a billing cycle, see what your bill is and then decide if you want to pay for the 10 degree increase.
If you were to raise the temperature 5 degrees all the time, I'd budget for a 20% increase. If you're just doing the 5 degree increase when you're home and awake, then budget for 10%. It should be less, but at least you'll be on the safe side.
Also, our monthly service charge is $10 and has nothing to do with the amount we use. Then we pay for actual gas used on top of that. If this is the case for you, you'll only need to figure the 10 or 20% increase on the energy cost. Example: if your service charge is $10 and your energy currently costs an additional $30, you're paying $40 total. If we do a 10% increase on the $30 energy portion, it adds $3 to your bill, making the total $43.
And it does make sense to have the temp lower at night and when you're not home, as you've been doing.
From the US Dept of Energy website:
A common misconception associated with thermostats is that a furnace works harder than normal to warm the space back to a comfortable temperature after the thermostat has been set back, resulting in little or no savings. In fact, as soon as your house drops below its normal temperature, it will lose energy to the surrounding environment more slowly. The lower the interior temperature, the slower the heat loss. So the longer your house remains at the lower temperature, the more energy you save, because your house has lost less energy than it would have at the higher temperature. The same concept applies to raising your thermostat setting in the summer; a higher interior temperature will slow the flow of heat into your house, saving energy on air conditioning.