The Wi-Fi works fine for most iPhone 5 users. It was fine in our tests. But a lot of people have been complaining that the Wi-Fi is awful and can't hold a signal. This should fix that right up for you.
This issue has been observed by people holding an iPhone 5 in one hand, and an iPhone 4S in another, and finding that the iPhone 4S gets full Wi-Fi bars while the iPhone 5 struggles to keep even just one for a few seconds.
WPA and WPA2 are newer encryption technologies than WEP, but they have a few more issues syncing on networks with older devices. If it's an issue, the newer WPA-enabled devices are supposed to be able to automatically switch back and use WEP. It's possible the iPhone 5 is having problems with that. You should be warned, however, that WEP is significantly less secure.
Just to be totally clear, this should only be used as a solution temporarily until Apple fixes the problem through a firmware update or another solution is found. Until then, know you're trading security from people trying to access your network for functional Wi-Fi on your phone.
The switch to your router is relatively simple. You'll need to access your router gateway, which should be easily found through Google. For example, most Linksys routers are 192.168.1.1, while Western Digital routers can be accessed by simply typing "wprouter" into your URL bar. From there, just go to the Wireless and Security options, select WEP instead of WPA, and enter your new password. All done. Hopefully your Wi-Fi issues will be cleared up. Did this work for you? Let us know in the comments below.