The 5 GHz band is more susceptible to attenuation than the 2.4 GHz band. My only experience with 5 GHz is with my '825, and with it even 50 ft can be an issue. Walls make it much worse.
The other, 2.4 GHz band should provide better signal level and pretty near the same speed potential when set for Wireless N Only. But you probably have lots of interference on that band from nearby wireless networks in your apartment building. To address that issue I recommend finding a freeware WiFi tracking program for either an Android phone or a computer (Apple removed them from the iPhone/iPod touch App store for some inexplicable reason, so an iPhone isn't an option). I use the free WiFi Analyzer on an Android phone and it works great.
Scan for local signals and see which channel is the least cluttered and try setting your router to that one.
Alternatively the '825 has a checkbox in Wireless configuration to Enable Auto Channel Scan. You can try checking that to see if it provides any benefit. I recall reading some critical comments about that setting, but don't remember details.
If none of this helps, and you can't move the router closer to the Roku, then getting a device to relay the signal is the only option that I can see as well.
Good luck.