OK, I have both.
Note 3:
Works fine on my Note 3 just as long as you have it set up to work and say the RIGHT THING. You can change your wake up command........
It should be in your start up apps, you can search your phone easily for that using the search function in settings.
S5 My sons works fine. Go into the apps/widgets sector by pressing and holding the screen, then add the widget for Open Apps (small circle with number of apps in it that are running still.)
Place that on your home screen.
tap it and go to the heading for "start up" APPs and add S-voice to your start up apps. Problem solved
OR
When you switch your phone on (I never turn mine off.........) Open S.voice and leave it running by using the back "button" to return to your home page.
It'll stay open in the background.
Very easy to sort.
PS.
Check EVERY menu item on a NEW phone and you'll be amazed at the functionality you don't know exists...........
Best of luck
(I also have Tab 2, 7 and 10.1 inch with Phone function and a Tab 3, 7 inch and will be getting the TAB S 10.5" very soon. Any questions on those devices feel free to message

I have 3 Samsung Smart TV's 65", 50", and 40"
I have 3 Samsung Laptops RF711, 17".
RF511, 15.6" windows 7, and a
Samsung Windows 8 15.6" Laptop can't remember the model number, sorry, but can help with Samsung related issues there too as I have rebuilt the operating system after an engineer caused total hard drive catastrophic meltdown and full data and OS loss, so Have bulit the samsung system with peripherals back up from Scratch.....
I am self taught but a long time Samsung Devotee so can help with most Samsung issues.
I even helped Samsung sort THEIR Allshare software out with file size issues an library retention and playback.
I Do Not Root, sorry............