Arduino hacked rc car, H bridge, logic voltage overwhelmed
That tutorial shows a Tyco R/C vehicle, which uses an RX2C decoder IC with outputs that can source or sink up to 6mA to drive H-bridge transistors. Typically the signals are coupled to the transistors through current-limiting resistors. Raising the drive voltage to 5V would just increase the Base current a bit and shouldn't hurt the transistors. 

Here is a partial circuit traced from a Tyco 'Canned Heat' r/c car, showing the RX2C and H-bridge motor driver. Each decoder output is coupled via a 1k resistor, which would limit Base current to less than 4mA at 5V.   



To verify that the higher voltage won't affect any components on your board you should trace out the circuit and and understand what each part does. Provided that they are all still within spec at the higher voltage it should be OK.

If you want to apply PWM then each output transistor in the H-bridge should have a reverse-biased Schottky diode from Collector to Emitter, to soak up back-emf spikes and recirculate current through the motor. If your your circuit uses FETs then you won't need diodes because they are built in to the transistors.