Samsung Galaxy S5 Mini is a great phone but you can make it much better by installing custom firmwares and mods on it. For that you will require official TWRP. This is for the Snapdragon variant and not compatible with the Samsung Exynos variant.
Here is how you install it. First download and install Samsung drivers from here. You will also need Odin and TWRP to flash the ROM. Turn of your device and go to odin mode [ Vol down + power + home button (all at the same time) ] release it when you see Galaxy S5 Mini Logo. Press vol up to confirm.
Installation instructions for TWRP for Galaxy S5 Mini
Now that you are in Odin Mode connect your device via USB cable.
Now open Odin3 3.09 or 3.07 that you have downloaded.
If there is a pop-up like Installing ADB drivers let it get finished it usually updates.
Make sure the COM : xx (xx is USB port number it can be any number so don’t worry about it,just verify COM is lit up).
Now select AP and browse to where you have .tar file and select it
Make Sure only Default Auto Reboot and F. Reset Time is ticked and nothing.verify twice only these 2 are ticked.
Click Start and wait for the process to end. DO NOT Interrupt during this time.
Once it says PASS. BOOT INTO RECOVERY USING VOL UP + HOME + POWER BUTTON.
How to Root Galaxy S5 Mini
Download latest SuperSU from here.
Copy the zip to Internal or external SD Card of your device.
Power off your device and press vol up + power + home button (all at once)
Select install zip from sdcard —>choose zip from sdcard —> scroll down and flash UPDATE-SuperSU-v2.xx.zip.