How do I use my dual band Wi-Fi card to connect to 5GHz and 2.4GHz simultaneously on Windows?

Just to be clear, that card can use either band, but it can't use both at the same time. That is, it's not "simultaneous dual-band" which is also called "dual-band concurrent". I'm not aware of any client card that is. Simultaneous dual-band support is something only APs do, in order to support legacy 2.4GHz clients and more modern 5GHz clients at the same time.

If you want your dual-band client card to automatically pick the best band, make sure both radios in your simultaneous dual-band AP are publishing the same network name (SSID) with the same security mode and same password. I recommend WPA2-personal a.k.a. WPA2-PSK, and I recommend AES-CCMP only; don't bother enabling TKIP (this may be called something like "WPA2/WPA mixed mode") unless you know for a fact that you still have an old product around from c. 2002-2003 that supports TKIP but not AES.

If you don't have a simultaneous dual-band AP, and instead have two separate APs (one for 2.4 and one for 5GHz), still make sure they're both publishing the same network name, with the exact same security mode and password.

Since both your AP and your card support both bands, you are free to select whichever one you want. However, you cannot connect both bands simultaneously. WiFi just doesn't work that way.

If you configured the SSID for both the 2.4GHz and 5GHz bands to have the same name, your laptop would only see one SSID, and you would only have one entry to connect to. But you still wouldn't be connected to both bands. Your laptop would "decide" to use one frequency or the other.

Now I'll interject my personal preferences here by saying that I believe your setup is optimal. I prefer to have the 5GHz band on a different SSID because then I can always be 100% sure that the 5GHz band is the one I'm connected to, and I don't trust the decision-making algorithm to make the correct choice. I've seen my laptop use the 2.4GHz band at hotels and other public WiFi networks even when the 5GHz band is available -- probably because the 2.4GHz band appeared to have better signal strength.

The 2.4GHz band is very crowded in most areas, whereas the 5GHz band is pretty much wide open almost everywhere I go. Moderate signal strength that is interference-free is usually preferable to good signal strength on a crowded spectrum. I can verify that result in my own house.

You might wanna check http://speedify.com/ (from the makers of connectify) while not allowing you to use two bands at the same time with one card, if you have two wifi adapters in your pc, you could connect to both, and then conceivably use their app to aggregate the connections. I've used it with connecting to multiple AP's before, not to the same one.