Hi George,
Motors that do any work have a high supply current and would kill a little 9V battery quickly. The relay and its wasted power could be replaced by transistors to drive the motors and LEDs without much waste. Electric wheelchars and golfcarts don't use relays, they use transistors to drive their motors.
I calculated the 180 ohm voltage-reducing resistors like this:
1) You said the relays are 5V ones but didn't tell us their coil resistance.
2) You measured 37mA when the circuit was without a voltage-reducing resistor for the relay, and a 9V supply.
3) The 10k resistor uses about 1mA from the 37mA total and the transistor's 10k base resistor uses another 1mA leaving 35mA going through the relay's coil.
4) 9V/35mA is 257 ohms, so I assumed that the relay coils are the standard of 250 ohms.
5) The rated 5V/250 ohms = 20mA for the relay as desired. You need to drop 4V across the voltage-reducing resistor at 20mA so 4/0.02 = 200 ohms.
6) But the battery voltage will quickly drop a little so 180 ohms will still provide the relay with 20mA and its rated 5V.
There are many kinds of batteries and charts showing their voltage dropping and life with different loads at
www.energizer.com .Click on Technical Info at the top, then Battery Type at the left. Energizer Alkaline is their most popular type but also look at their new disposable Lithium AA cells. They are expensive but hold up their voltage while discharging for a very long time. I got some free samples by doing a survey for them. They wanted opinions about how much to rip-off, err, price them. :lol: