I have been trying to root my Galaxy S5 Active for a few days. Finally found the way to do it. Towelroot will work, but not with that ROM. Follow these instructions and it should work for you without any problems...
Before doing the following, remove "Busybox", "Towelroot", "SuperSU" and "Xposed Installer" from your device. Download the apk files and install on your memory card. Then make a backup in Titanium Backup (or your preferred method/app).
1. Find and download the Official ROM made before June 26th for your device from SAM MOBILE. Once downloaded, unzip files.
2. Download Odin version 3.09
3. Download and install SAMSUNG USB drivers.
4. Put your phone in download mode (with phone being off, press and hold HOME button, VOLUME DOWN then POWER button) then connect to Odin.
5. In Odin, once your device is found, making sure only "Auto Reboot" and "F.Reset Time" is checked, click and load the MD5 file on the AP in Odin 3.09 or PDA on Odin 3.07 (second one down on right).
6. Click start on Odin AFTER the USB drivers have been fully installed and once Odin recognizes the device.
7. After the installation says "Finished", remove your phone from your computer.
*I did not have to set mine up as a new phone as I normally would after a new ROM install. Instead, it came right back on as if I didn't do anything.
8. After the phone comes back on, install in order:
A. Towelroot
B. SuperSU (reboot)
C. Xposed Installer (reboot)
1. Inside the "Framework" option, click "Install/Update" (reboot)
D. Safestrap 3.75, then inside Safestrap, click "install recovery" (reboot)
*At this time, upon reboot, you should see the Safestrap come up*
E. Wanam Xposed (reboot)
1. Back into the Xposed Installer, inside the "Modules" option, click all and then... yep, (reboot)
If you would like, you can install and run the Root Checker from the Playstore.
***I AM IN NO WAY HELD RESPONSIBLE FOR ANYTHING THAT HAPPENS TO YOUR PHONE. I AM SIMPLY AN AVID USER THAT PAYS ATTENTION. AFTER SEARCHING HIGH AND LOW FOR 3 DAYS, I USED THIS ON MY AT&T VARIANT OF THE GALAXY S5 ACTIVE AND THIS WAS THE ONLY WAY I FOUND ROOT AND SAFESTRAP TO WORK.***