I just started having the same problem on a friends galaxy s5 and just started reasearching this issue.

One thing i can tell you is that i beleive its started happening right after we started messing with the apps "kies air" and "airdroid" which are supposed to be completely safe to download... I tried uninstalling the apps, going into settings>app manager>all apps> scroll down to screen mirroring > clicked force stop> did same in usage manager from apps and nothing!!!! Still working. Everytime i turn it off and leave and open it again it goes back to screen mirroring on!!!

Did you download either of those apps or something similar?

 

we are both idiots, i just realized by looking at running services that everytime you choose the screen mirroring icon in settings, as soon as the screen mirroring options screen pops up it will always say on... The reason for this is because everytime you choose the screen mirroring icon to turn it on or off it will automatically turn it on.....
In other words just turn it off and back out .... It will stay off.. The reason we thought it was being turned on was because everytime we choose it to check if it is turned back on... It is going to immediately auto turn on and start scanning for devices lol i dont know if u understand what i am saying but just do this\

1. Select the mirroring icon in settings and turn it off then back out and dont open it again to check if it stayed off because it will turn it back on... I also read this in another website so we are not the only idiots....

2. Check your services or processes if u need proof and you will see that it is not running unless u turn it on and leave it on before you back outof setting

 

we are both idiots, i just realized by looking at running services that everytime you choose the screen mirroring icon in settings, as soon as the screen mirroring options screen pops up it will always say on... The reason for this is because everytime you choose the screen mirroring icon to turn it on or off it will automatically turn it on.....
In other words just turn it off and back out .... It will stay off.. The reason we thought it was being turned on was because everytime we choose it to check if it is turned back on... It is going to immediately auto turn on and start scanning for devices lol i dont know if u understand what i am saying but just do this\

1. Select the mirroring icon in settings and turn it off then back out and dont open it again to check if it stayed off because it will turn it back on... I also read this in another website so we are not the only idiots....

2. Check your services or processes if u need proof and you will see that it is not running unless u turn it on and leave it on before you back outof setting

 

One bit, don't bother, it is built in feature so THE THIEVES IN THE CIA CAN ROB YOUR LIFE IF THE WANT TO!! RAYTHEON, HONEYWELL AND BOOZ ALLEN HAMILTON ARE BIG ON USING IT AT MACDILL WITH OUR OTHER TOP SECRET PRIZED POSSESSIONS!! THEY ALSO GAVE OUR TOP SECRET PRIZED POSSESSIONS AWAY FOR TO THE BACKWOODS COMMUNIST PARTY (AKA WASHINGTON D.C. CIA AND NOW MACDILL/SOCOM HAS BECOME THE WASHINGTON D.C. CIA)
JIM NEELY WHITE 53 OLD HETEROSEXUAL MALE, COVERT CIA AGENT SINCE 5/17/1997, FROM WEBSTER FIELD, ST. INIGOES MD, LEFT SOUTHERN MARYLAND ./1997, NAVY TECH BADGE UNDER CONTRACT N00421-97-C-1000, 1997-1999, CONSIDERED AN EXPERT AT IFF AND COOPERATIVE ENGAGEMENT CAPABILITY OF THE NAVY

 

If you want to mirror your screen onto your TV, just get Chromecast and download the app. Theirs a BETA option to cast whatever is in your screen to your TV. It used to suck because the picture and sound wouldn't sink well unless it was a native app like YouTube or Netflix, but now they sink perfectly. In fact, as I'm typing this on my S5, I'm watching 'Watchmen' on my projector, mirrors from my phone from a 3rd party website.