Seems to be some confusion here, and I think it's semantics which is the culprit.
Dual-band refers to WIRELESS, and has nothing to do with WIRED.
If you use a wired connection (with an ethernet cable) from your PC's ethernet connector on the wired NIC to the 1-4 LAN ports on your router, this is completely unrelated to the router's wireless capabilities, or the PC's wireless NIC capabilities which may also exist in addition to wired (separate from its wired NIC).
The speed of the wired connection (from PC to router) is a function of (1) the rated speed of the router, (2) the rated speed of the NIC, and (3) the type of ethernet cable you're using. If your router is only rated 10/100 then it doesn't matter what your PC and NIC are capable of, you will only get at most 100Mb/s speed to the router. Similarly, if your router is gigabit capable (i.e. 10/100/1000) as is your NIC, but you're using
CAT5 cable which cannot support speeds above 100Mb/s, you'll again only get at most 100Mb/s speed to the router. You need to use CAT5e or CAT6 cable from PC to the router to get faster than 100MB/s wired connection speed.
Wireless is entirely separate. Dual-band refers to 2.4Ghz vs. 5Ghz connectivity, but does not describe the actual "connection speed". Connection speed is more tied to the wireless protocol used over that 2.4Ghz or 5Ghz connection pipeline, namely 802.11a/b/g/n/ac. Each of these unique wireless protocols is capable of progressively faster wireless connection speeds, but you need a wireless router that supports those faster protocols, and over one band or the other or both (i.e. 2.4Ghz or 5Ghz).
In general, the 5Ghz band supports faster wireless connection speeds than 2.4Ghz, but is more vulnerable than 2.4Ghz to "interference" in the house and in general has shorter distances for reliable high-speed connections.
And of course, there is absolutely no guarantee at all that even with all the proper equipment and capability in place, that the physical characteristics of your home will support maximum wireless connection speeds over either wireless band, depending on distance to the wireless router, physical makeup of interfering walls or floors, etc.
Finally, just because you have high speed connection to the router (via wired or wireless), that has nothing to do with the actual DOWNLOAD/UPLOAD speed you get to the Internet itself which must further go through your modem and be handled by your ISP through whatever service tier level you've paid for. This variable is directly tied to your ISP.
Note that within your LAN (managed by your router), inter-PC and inter-device connection speeds are a function of wired vs. wireless, and ethernet cables used, and router capabilities as well as device capabilities. Outside of your LAN (i.e. through the router to the modem and out to your ISP and the Internet) you're now governed by whatever speed you've purchased from your ISP.
Bottom line: if you want MAXIMUM LAN CONNECTION SPEED (for the home PC's and devices within your home LAN network), use wired when possible along with CAT5e/CAT6 cable and a gigabit router (10/100/1000).
If you want maximum wireless speed, your wireless devices need to be relatively near the wireless router (or access points) so that 5Ghz band can be used, and need to be capable of 802.11n/ac speeds (N150 and N300 and N600), which needs a wireless router (or access point) capable of supporting 802.11n/ac protocol.
Anything less will see reduced or compromised wireless and wired speeds.