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You are lucky it lasted that long! Costco sells batteries for the RX, I have one. Also any large auto parts chain store will have them and some will do the labor for you.
Costco carries the best warranty in town (72 months) for their batteries with full refund if it dies/returns within 36 months. Everything after 36 month is on pro-rated basis.
The standard vehicle warranty was 4 years or 50,000 miles, whichever came first. All 2013 models are now beyond their standard warranty.
Essentially correct ... BUT ..
The actual time clock starts with "Date in service" .. the day the dealer sells the vehicle. Dealers do not get the old production model with the start of the new model year (production switch over), but they can have an older model with them and the sale can happen afterwards. Demos and employee loaned vehicles can be in this pool too.