Well that depends. First can you max out your internet connection? If you have a 20Mbit connection and you can get that over your present wireless adapter, then you aren't limited on the internet. Second, do you have more than one computer on your LAN that you transfer files between (this computer and another), if not then you aren't limited on your LAN either. In these situations there would be no need to upgrade your wireless adapter.
However if you can't utilize the full bandwidth of your internet connection and / or you regularly transfer files between this computer and another computer on your network, then it may be advantageous to upgrade your adapter.
One thing to consider though is the distance this computer is from the router. The 5GHz band doesn't penetrate walls / floors / obstacles as well as the 2.4GHz band. This means if you are getting a mid to low power connection to your router on the 2.4GHz band, you may find it difficult to get a connection on the 5GHz band, or it'll connect but could be slower than what you are getting on the 2.4GHz band.