You can look up 5 and 7--series motors on a number of websites and compare dimensions.
This is a Mabuchi datasheet for some 550 motors:
There are a lot of different variants: 5-series (550, 545, 540) and 7-series (735, 755, 775). The "7" designation refers to the diameter. The 7-series motors are basically all ~42mm diameter (excluding torque sleeve) and has a M4 thread hole with 29mm spacing, and they all have a 5mm shaft. The 5-series are 35mm diameter, M3 thread @ 25mm spacing, and all have a 3.175mm shaft. The 550 vs. 545 vs. 540 are just different lengths (550 = ~55mm long). Same with 775 vs. 755 vs. 735 -- 755-series motors are about 58mm long. 775 are about 66-68mm long.
Yours looks like a 550 motor, and probably a 32DP (or m0.8) pinion -- though if you can measure the diameter you can verify it's not 48DP, mod0.6 or something else odd. "32DP" is diametrical pitch; theoretically a 32-tooth 32-pitch gear is 1" diameter. A 16-tool 32-pitch gear is 0.50" diameter.
Here's a 775 motor that has a datasheet for comparison (it's low-speed, not a good fit for a ride-on toy, but the case size is standard):
http://www.robotshop.com/en/rs-775-moto ... ifications
F-150 - 24-36V with homebrew 100A variable-speed motor controller, 4x 775 motors (no, it's NOT all-wheel-drive--look HERE
for more details!)
Pink Rocket Princess Mustang - 15mph, 36V, 4x 775 motors, homebrew PWM controller rev 2....
Hurricane - 24V w/50A step-down controller, 775 motors