Rather than hooking stiff coax directly to the radio with an adapter, here are two good accessories.
The first item, the BNC adapter, allows connection to the cable, second item above, but also now you can attach any of the many good BNC antennas, or other coax with BNC.
The second item, the pigtail is 4' long, low loss LMR-100 coax. It goes to BNC on one end, and SO-239 on the other. There is a similar one with male SMA. If you used that you would need a double SMA-F barrel connector. Since you need an adapter one way or the other, might as well be BNC. That way you only need a 1/4 turn to connect or disconnect.
With this setup you can connect to your base antenna coax. The long flexible pigtail lets you handle the UV-5R like a mic, and no stress on the antenna connector.
Or as I do, use it in my wife's car, with a mag mount antenna, and the pigtail connects to the coax coming off that magnetic base. It is a NMO type mount, so I have a little 14" Diamond NR72BNMO quarter wave. It does very well with just 1 watt, Low setting.