You may be owning a Samsung Galaxy S5 currently, and you may be a geek too! And the network carrier of your Samsung Galaxy S5 may be AT&T, or may be Verizon. Now, if you fulfill all the three terms- you have a AT&T/Verizon Samsung Galaxy S5 and are a geek, then there is a good news for you. The XDA developer Geohot has provided the solution for your Samsung Galaxy S5 root, if it is on AT&T or Verizon carrier. There are several other ways for the Galaxy S5 root, which work for other models of the Samsung Galaxy S5, such as that of T-Mobile/Sprint, or other international version models. The XDA Developer Chainfire has posted for this, some months ago.
The root method, presented by Geohot will also reportedly work on other devices too, such as the LG Google Nexus 5, Samsung Galaxy S4 Active, LG G2, Sony Xperia Z2, Galaxy Note 3 or any other smartphone which has a Kernel build date of June 3, 2014 or before, but there are some issues reported in some of the devices. As there is no need to be stated that the root method is really very useful for the removal of several bloatwares in its device (these may be very useful for many of us though!), you can have this trick to root your AT&T/Verizon Samsung Galaxy S5 now.
Geohot is famous for providing the first unlock for iPhone before, and is one of the top developer among the XDA Developers. He has made the announcement that he can deliver a solution to the Galaxy S5 rooting predicament, which is almost as simple as sideloading an APK on your smartphone. The root method has been named as towelroot method, and will require to download an APK and install it in your smartphone.
You can see the complete root method for AT&T/Verizon Samsung Galaxy S5 here,or the root for other Galaxy S5 models here.
Good luck with your rooting!