Hi Christina.
Generally. On I have a BT router. With my 5000t connected via Wi-Fi.
This is without any problems. I haven't had hardly any speed drop off, or internet drop out. My router is a series 4( not the newest ). If you have a connection problem from your box to the router there is a way around it.
B T has a Wi-Fi range extender box. It's simple to set up you plug it into the mains anywhere that's a lot nearer to your 5000t than your router.
You then link it to the Wi-Fi side of your router like anything using the router password.
Then you would set up the Wi-Fi on the5000t linked to the extender.
This bit can be a bit tricky, when you link the 5000t to the extender remember,the extender has a different name than your router.
Going back to setting up the extender there are 3 lights 1 red that's also marked too near, another red that's marked too far. want the only green light to be on that means it has a good lock onto your B T router.
My situation was the reverse of yours, and I had to set my extender on the other side of our house, but upstairs. If the extender is next to your 5000t you can then have a choice of Wi Fi or ethernet connection between the two of them.
The extender really does need a very weak signal from your router in order to boost it. my BT booster is twin channel as is my router.
Of course, you may be ok and when doing the first install & set up the 5000t may find your router itself, rather than going down the signal booster route. Good Luck.