There isn't much information about this. I found an equally frustrated person in this thread:
https://forums.arcade-museum.com/threads/williams-transformer-in-data-east-pin.217690/
I haven't done this, and I probably wouldn't. I would wait until I found a fire-damaged or flood-damaged machine with the correct 10-5003-00 transformer and use it.
But, if I absolutely HAD TO...
I would find another 5003 transformer, and measure the actual AC voltages coming out.
I would take my substitute transformer and make sure the voltages were all present, and within a couple of volts.
I'd wire it in, but here is the problem... Transformers supply what the output (the pinball) requires. And if the 70V winding on the Data East transformer was rated for 10 AMPS, and the substitute transformer was rated for, say, 4 AMPS, the substitute transformer is going to try it's best to supply what the pinball needs.
Generally power distribution is over-specified, and you'll be fine. However, suppose the pinball you are putting the substitute transformer into requires 5 AMPS and your (replacement) transformer was only specified for 4 AMPS. This would work, maybe forever without trouble due to the transformer being over-specified, or maybe not.
And what happens when the answer is 'not' is that you'll have a bubbling mass of goo come out of the transformer, a horrible burning electronics stink, and a VERY SERIOUS fire hazard.
Which is why I'd probably never substitute a different transformer unless I could find out the actual power specifications of each winding for each unit, and make sure the replacement is specified the same or higher on every winding.
It's all in fun until you burn down someones house. I wouldn't be taking the chance.