There is little chance on running an a/c, 13.5 or 15,000 Btu with an extension cord from a 15 amp home service outlet. Starting current on a 15K unit is over 20 amps and running current is about 16 amps. The Dometic a/c IB says install with 12 AWG wire, not exceeding 25 feet for hook up. 12 AWG wire is rated for 20 amps. Your 30 amp service wire is 10 AWG which is rated for 30 amps. 2 a/c, running at the same time will 'consume' ~32 amps
On a small, 30 foot or less, 5er, a single 15,000 Btu a/c may be enough for most uses. With a 30 amp service, you should be just fine. Our 5er has 50 amp service but for a couple more weeks only a single 15K a/c. With that, we have seldom used that heavy, unwieldy 50 amp, multiple conductor 6 AWG cord but have used adapters and a simple 30 amp cord with 100% reliability on all gadgets. That added 13.5K Btu a/c goes on the roof and my workout at each stop will then begin.