Probably not.
Unfortunately, you did not bother to mention what you planned to do with it: use it as a primary device, a backup device for yourself, for a family member, a replacement unit for another iPhone 5S, as a media player, etc. so we will just have to address the mundane technical points without any relevance of your use case.
The iPhone 5S design is 3.5 years old, debuting in September 2013. The iPhone SE is a far superior device in all respects: better silicon, better cameras, better WiFi, better cellular support, better battery performance, Touch ID, Apple Pay, and more. All in the same chassis. If you want that size phone in your pocket, the SE is the one to get today.
Depending on the actual iPhone 5S unit you get, the battery may need replacing soon, so you'd be wise to figure that cost in. It would be highly unlikely that the device would have a 1-year manufacturer's warranty.
Also, the iPhone 5S is nearing the time when the latest iOS won't be supported on the device. The current iOS 10 supports devices going back to the iPhone 5 (September 2012 release). Even if the upcoming iOS 11 supports the iPhone 5S, it is highly possible that iOS 11 will make the phone run slowly. This is rather typical for the oldest generation of hardware supported on any given iOS release.