Higher is fine. If you really want to plan things out you could do some research into exactly what bands the 5 GHz wireless-N protocol uses so that when you one day, presumably, get a 5 GHz wireless router you won't run into the same problems.
FWIW, we just bought a 6 GHz phone system since we were having troubles with our wireless dropping whenever the phone rang. Changing channels wasn't really much of an option due to all of the other neighborhood wireless networks. The 6 GHz frequency does not at all interfere with the 2.4 GHz wireless router and also allows us to upgrade to a 5 GHz wireless-N router in the future.
Have you tried changing the channel your router is using? If you haven't, before buying a new phone system, I suggest you log into your router and try diferent channels to see if you can find one where there is no conflict. Most people seem to recommend Channel 11 to avoid conflicts, I have found that Channel 1 seems to work best for me for some reason, and I do have a 2.4 GHz wireless phone on my desk about 4 feet from my router.
If you do decide to buy a new phone system,I think pretty much any 5 GHz or higher system will not conflict.
Just something you can try before you invest in a new phone...