This root method works only on Samsung Galaxy S4 I9500 and I9505 models running Lollipop 5.0.1
Before you start, please check if your Galaxy S4 is supported by going to Settings/About Phone
Rooting voids device’s warranty. Users should proceed at their own risk.
Prerequisites:
• The device should have at least 60% charge left on the battery.
• If you have Samsung Kies program in PC, Kies should be completely turned off to not disturb all the process.
• USB drivers must be installed on PC (if Kies are in PC then drivers are already installed).
• USB Debugging must be enabled on the device. To enable it go to Settings/About phone and keep taping on Build number until you see Developer mode has been turned on. After that go to Settings/Developer Options then check USB Debugging.
Tutorial:
1. Download to PC Odin3 v3.10.7 and extract it.
2. Download to PC Philz Touch Recovery depending on your device model.
Philz Touch for I9500
Philz Touch for I9505
3. Turn off Galaxy S4 and boot in to Download mode by pressing and holding down the Volume Down, Home and Power buttons together. When a warning screen is displayed release all buttons and press the Volume Up button to enter Download mode. 
4. Run Odin3-v3.10.7.exe as an Administrator and then connect Galaxy S4 to the PC via USB. Message showing Added!! will appear in Odin’s message box, if not, try another USB port. If the issue persists, try reinstalling the USB driver.
5. Click on the AP button and select the Philz Touch Recovery (a .tar.md5 file), which was downloaded in step 2.
6. In Odin, make sure that the Auto Reboot and F. Reset Time options are checked while Re-Partition must stay unchecked. 
6.1 Click Start button in Odin to begin the process.
6.2. After the process is complete, Galaxy S4 will restart and a PASS message with green background will appear in the left box at the top of Odin. 
7. Turn off Odin and unplug USB cable from device.
8. Using device, download SuperSU.zip file.
9. Turn off Galaxy and boot in to Philz Touch Recovery by holding the volume up + home + power buttons all at the same time till the recovery menu show up.
10. Select Install zip then Choose zip from /sdcard and locate SuperSU.zip file, which was downloaded in step 8. 
11. Flash SuperSU.zip file and reboot your device by taping on Reboot System Now.
12. You should found SuperSU app on the screen.
Congratulations for successfully rooting Galaxy S4!
