So are you suggesting that the servos themselves cause a spike when working ?
Yes.
I haven't used this hardware before, but from experience with switching relays, solenoids and transformers ... its better to have a separate power source from the electronics. Even if they share a common ground, its better to have separate 5V rails (one for the electronics, one for the motors). The motors don't need accurate voltage regulation, so this gives more alternatives for power sources.
EDIT: If its just not feasible to have separate power supplies, then I would set the existing supply quite low (even as low as 4V) prior to testing. Some extra capacitance on the 5V rail may help.
Does the hardware/documentation show information using separate power connections?