This app was mentioned in 16 comments, with an average of 1.31 upvotes
This sounds like something AllCast Receiver can do, but I haven't used AllCast or AllCast Receiver in over a year.
I think these are two mediocre options that might help.
https://play.google.com/store/apps/details?id=com.koushikdutta.cast.receiver
You can actually use an app like this: https://play.google.com/store/apps/details?id=com.koushikdutta.cast.receiver&hl=en
I've never used Remix OS but I'm assuming you can install playstore apps or at least sideload them?
What would you guys think of installing Allcast Receiver: https://play.google.com/store/apps/details?id=com.koushikdutta.cast.receiver and using Allcast on my phone to cast to the old phone? I'm gonna try it when I get home today
You could use something like AllCast Receiver to use your Android phone as a Chromecast receiver and cast content like YouTube videos from your iPad to your Android phone. Then you can browse YouTube, cast a video to your Android phone, and then go play a game on your iPad while the video plays.
Never tried this before, but have you looked into the AllCast app?
https://play.google.com/store/apps/details?id=com.koushikdutta.cast.receiver
I haven't used it so I can't speak for it.
You don't need to root the S5.
Linkme: Allcast Receiver.
EDIT: https://play.google.com/store/apps/details?id=com.koushikdutta.cast.receiver
Will AllCast not work? https://play.google.com/store/apps/details?id=com.koushikdutta.cast.receiver
Here are some ideas from a fairly recent r/android thread
If you like to tinker and dont mind a bit of upfront cost for a few extra parts, you could make a smart thermostat
Gaming
If you like old school emulators and already have a wired (or wireless but could be a little trickier) game controller you could buy an otg usb to microusb adapter from amazon and have a portable gaming set up. I was able to get SNES emulators to work with a wired 360 controller and a generic one i picked up from goodwill. Unfortunately with my adapter it only accepts one input at a time despite multiple ports so I couldn't set it to stay charging and play simultaneously. If you use wireless bluetooth gamepads you could use a hdmi adapter to connect your old phone to a tv.
Portable Workstation
You could also use the otg adapter with a wired keyboard if you are in a pinch or away from a computer.
VR
If you are interest in vr but dont have triple digits of disposable income to try it out, you could buy some google cardboard and use the old phone as a vr headset with all these apps to choose from
Home theater
If you have your phone connected via hdmi to your tv you could use Allcast receiver to send media to your old phone to display on the screen or use Kodi on the old phone and a kodi remote on your new phone to have a very affordable home theater experience.
Edit: more ideas