InSilence, i'm afraid this issue impacts any iPhone 5 device downloading large files, you can see this by running a test with a large iTunes app install or Dropbox file and you will also see the same performance. The only reliable work around for this specific issue is to pop a proxy server on your network and run your traffic via it (see previous posts with ideas for proxy options and how to setup). A few of us are 100% certain the issue is either a driver issue, or worse a hardware issue (that would not be able to be resolved), this conclusion has been identified after a number of people have completed extensive network testing (including running packet sniffers via a few different kinds of WIFI devices), key finding is an ever reducing TCP window size is causing the issue. The same test on iPad 3, iPad 2 and iPhone 4 don't show the issue, so it's not the network or networking equipment (I've tried quite a few networks also).
Sadly as my telephone support period is over and the genius bar has proven useless on two occasions I can't see any way to get a resolution on this wide spread and highly frustrating issue.
I've given up, either a driver fix is included in a future release or Apple confirms that it's a hardware issue that can't be fixed (I doubt this would ever happen). If anyone else has another support channel that will be able to understand this more complicated problem (i.e. it's not a simple user issue or configuration related) please use it, and use it as many times as you can. If you are still within your initial enhanced support window, don't waste it. This issue, combined with the fact that WIFI sync just doesn't work (oh not to mention the ATH.exe high CPU bug in iTunes) basically means that any larger video Podcasts are almost impossible to download (either directly or via iTunes, unless I remember to plug in iPhone in a few times a day). If Podcasts are a big deal for you, as they are for me, I would honestly consider taking a newly purchased phone back and waiting to see if they fix in the next iPhone release. Another option would be to use another iOS device that you might have if like me you are stuck with an iPhone 5 that is useless in terms of WIFI reliability and usability. Sad that Apple doesn't care about this (yes I understand they don't read these threads), given that many of us have gone back through support channels only to have the issue largely ignored.
(edited as I stupidly included references to a future release of iOS, I have removed all references).
I have had the opportunity to compare 2 iphone 5s that both suffered horrendous download speeds when downloading large files on Dropbox. One was upgraded by its developer-owner to a "future" release, and its Dropbox download now flies. Verified a number of times. If I'm not allowed to post information like this, I apologise - not sure what the rules are...