To put it simple; There is one advantage with the RT-AC5300U over RT-AC68U and that's Tri-Band/Smart Connect. I own RT-N66U, RT-AC66U, RT-AC68U and RT-AC5300U and I have also owned RT-AC3200. In terms of range they are all pretty much the same in my experience. I would actually give the edge to the RT-AC68U, especially on 5GHz/802.11ac but they are all in the same ballpark.
Compared to the RT-AC68U, the RT-AC5300 will give you a slightly faster SoC (you won't even notice this unless you are using OpenVPN etc..), MU:MIMO (you will most likely have no MU:MIMO clients for a long time, not to mention the fact that the MU:MIMO performance and stability is rather poor and the entire feature is still labeled as "BETA/Experimental") and last but not least Tri-Band / Smart Connect.
Everything else will be the exact same. The software/firmware is the same. The wireless range, stability and performance is pretty much the same. And even though the SoC is slightly faster, you will properly not notice as the only thing being bottlenecked by the SoC at this point is VPN.
In the end, you pay for two things; MU:MIMO and Tri-Band / Smart Connect. As MU:MIMO is still experimental and from what
Thiggins have heard it might seem like Broadcom have pretty much abandoned MU:MIMO on this first wave of MU:MIMO chipset from Broadcom. So it might seem like it will stay BETA/Experimental, unstable and lacklustre for eternity.
Tri-Band / Smart Connect on the other hand is working really good with the RT-AC5300. It was really bad on the RT-AC3200, but it seems like they've figured it out with the RT-AC5300. Tri-Band / Smart Connect is a really great feature if you have lots of wireless devices in your home. Having the router auto-steer your devices so slower devices won't bugle down your wireless performance is great. With the trend of having everything connecting using WiFi this feature is awesome. I have a Withings Smart Body Scale using WiFi, I have a Harmony Smart Hub using WiFi, I have a Ring Video Doorbell using WiFi etc.. All these devices don't require any high performance so having the router steering them to their own wireless NIC on the router instead of having them competing with devices like my MacBook's, Apple TV etc that requires high bandwidth is great and from my experience Smart Connect on the RT-AC5300 does all this very well.
In your situation, if it's all about improving range the RT-AC5300 won't do you any good compared to the RT-AC68U. Then you would be much better of by grabbing a second RT-AC68U and utilise it as a dedicated access point.