IOS 10 is the latest software update by apple announced at WWDC conference earlier this week. IOS 10 has some great features like enhanced user experience, redesign, more control to SIRI, enabling quick type , no more slide to unlock they will be replacing it by touching home button options and many more.
IOS 10 is already available to developers and they are testing it out. For this, you need to have a developer account. But Apple will be opening a program in July where they will allow all the users to test the beta version but make sure before downloading it, as it is beta version it may consists of bugs and make screw your device.
You can wait till September for a free update where they will be releasing it officially along with the new MacBook & I phone devices. This 3-4 months delay is usual, as they want to test it out with developers who are ready to test beta version and give feedback to them of any bugs or improvements rather than releasing it directly. so it's better to wait until September.
IOS 10 will be releasing to following devices
IPad 4 , iPad Air, iPad Air 2, iPad Pro (9.7in and 12.9in) and also to
iPad mini 2 and later iPad mini 2, iPad mini 3, iPad mini 4
iPod touch 6th generation
iPhone 5, iPhone 5, iPhone 5c, iPhone 5s, iPhone 6, iPhone 6 Plus, iPhone 6s, iPhone 6s Plus, iPhone SE
As you can see your devices iPhone 5S/5C is listed above, so yes there will be a free upgrade to your device.