This worked for me as i searched and searched! Finally my iPhone 5 is complete!
Settings> Wi-Fi > Blue icon next to the network you’re connecting to > Scroll to the bottom > Set your device’s HTTP Proxy to Auto (leave Url blank)
After this, try speed test again! Snappy!
I got this from iphone5issues.net
This did not work for me either.
So.... My 5's Wi-Fi worked pretty good out of the box, and over the weekend. Come today, it didn't work at work. I thought it was work. We have problems all the time. Then I get home, and it's not any better.
Sometimes there is a glint of activity, but not enough to update apps. I thought maybe it was my router. I reset the router, nothing.
Since it was working fine over the weekend, I feel like something broke overnight.
UPDATE: I noticed GPS was active. I killed all apps. Rebooted. Then not at first, but within 10 minutes, something healed and now it's running good again.
This is strange. I hope it's not a common thing. I hardly ever had to reboot my other iPhones.