Hi Goldfinch, well done on getting back into the running.
i wouldnt worry about speed. there are lots of people on here (me included) who would take an hour or longer to run 5 miles, or did when they started. the key to it is enjoying it, and it sounds like you are, plus getting fitter and battling your illness at the same time (dont have any knowledge of this, sorry). i have been running about a year and am just starting to see am improvement in times over shorter distances (up to 3 miles).
if you want to increase speed specifically have you looked at any training plans? there are lots around, just find one that suits you. a mix of long/short and fast/slow/varied runs seems to be the way to go, and keeps it interesting.
or how about running with someone else, a partner, or a running club. i definitely run further and faster with other people.
just keep on enjoying it and speed will come in the end.