I agree - the UA
website is usually reliable when it comes to the a/c type.
I doubt the 737-500 is accurate! It appears to be 738s and 739s on EWR
depending on the flight: the seat map for your flight is usually the definitive way to verify the planned a/c type.
For historical information, you can check the flight status page at UA
.com and plug in your flight number (assuming it's currently in use operating the same service) to check what's currently flying that service, +/- a day or two: one of the best features is that it displays the tail number so you can verify the actual ship used/planned.