Matthew,
As far as I know this is a site-wide issue, that would require a very considerable code hack to only change the settings for assigments. I have recently changed the time appearance across our site and even that appeared to only be possible by editing the language config file (in my case) /lang/en_utf8/langconfig.php (with considerable care). Although I believe the Calendar module has its own override settings, these don't apply to assignments or elsewhere.
My main concern was that the time 05:00pm means virtually nothing in the UK, and is a real source of confusion, as times are either 05:00 and 17:00, or 5:00 am and 5:00 pm.
If you decide on a site-wide change you may find MDL-11094 useful, especially the link to the PHP time definitions that Eloy (stronk7) posted in there in response. I found that info so vital I pasted it as comment lines into langconfig.php, in case I need to revisit it!
Regards, John