Jim,
There is a photo of 5937 in the Milwaukee Road Color Guide Volume 1. This is a different body style (no RPO), just a baggage/express compartment and 12 windows in the passenger area. This photo isn't the best and the colors on the car have faded, but the lettering on the side (REA) is white. Not sure about THE MILWAUKEE ROAD part, but my guess is orange (like the passenger cars). The sides are a light orange (like a light reefer orange), the letterboard and window frames in the passenger area are maroon (which you can also see in your photo). It appears that the front of the car is a darker orange (like the diesel locos). I don' see a black stripe around the letterboard. The roof is a grimy black/grey.
Hope this helps.
Best wishes, Dave