Now, it has Cydia for iOS 8+ versions of your iPhone 5S besides iOS 8.2 & iOS 8.1.3. It is ready to use three jailbreak tools such as TaiG, PP Jailbreak and Pangu8. Use following link to get instant jailbreak supports of those three jailbreak tools.
The Apple has released iPhone 5S with iOS 7, as they promised on September 18th of 2013. Now, it is available iOSs 8.1, 8.0.2, 8, 7.1.2, 7.1.1, 7.1.0, 7.0.6, 7.0.5, 7.0.4, 7.0.3, 7.0.2 & 7.0.1 only. Apple has released iOS 8.1 as the latest released for the public. As i think, this is the more valuable iDevice from all the devices after the iPhone 6 and iPhone 6 Plus. There are available many new feartues such as Super HD camera and screen, Dual LED flash, Better battery with long life, NFC, Possible updates include an IGZO screen for Retina+, 4” IGZO screen, 652 pixels per inch (2272*1280), 128 GB storage, Wireless charging. It is based on new A7 chip, iPhone 5S has came with 3 colors. It is little bit similar in the iPod touch model as I think. So, there are available many new software and hardware features with iOS 7+.
You can jailbreak iOS 7.1.2 as well with the new Pangu previous tool versions. It was available Cydia for almost all iOS versions, which is available on your iPhone 5S such as iOSs 7.1.2, 7.1.1, 7.1 with Pangu 1.2.1 Windows version & 1.2 Mac version, before release iOS 8. Still, you can’t jailbreak iOS 8, 8.0.2 & 8.1 for Cydia. iOS 7 versions can jailbreak. Use following guide to download and install Cydia for iOSs 7.1.2, 7.1.1 and 7.1 devices.
It is available Cydia download for iOSs 7.0.6, 7.0.5, iOSs 7.0.4, 7.0.3, 7.02 & iOS 7.0.1 on the iPhone 5S with Evasi0n 7 1.0.7 tool. Windows and Mac users can jailbreak this to install Cydia. Here are the links for both Windows and Mac users of the new Evasi0n 7 1.0.7 guides. This tool version is not support to jailbreak iOSs 7.1 or 7.1.1 or 7.1.2.
So, enjoy with Cydia.