Cannot root Verizon Galaxy S5 with towelroot I have downloaded towelroot tr.apk for my Galaxy S5 from Verizon which I purchased recently. 

I have heard of people having success with towelroot on their S5 devices bit for some reason I have been unsuccessful so far in rooting my device.

If I press the "makeitra1n" button I receive an error message saying my phone is not supported.  

I did some research and found you could change the settings of the program

This article supplies instructions to change the modstrings : http://www.naldotech.com/how-to-fix-towelroot-phone-isnt-supported-problem/

But after trying all codes I still have no success, occasionally I get another message asking if my device is connected to the internet.

has anyone else shared this problem?
The vulnerability towelroot used has been fixed within Android 4.4.2. Check your version.
Plus, as you can read here, geohot, developer of towelroot, now works for Google, so probably there won't be updates.

I wouldn't recommend any other root method: it could invalidate your warranty. See this article.