C.D.
Hello - I feel for you girl - those first couple months are sooo tiring. Ok so I would try to cut out the diet coke for at least a week. Also - make sure you baby is getting enough sleep in the say. Normally when this happened with my son it was because I had not let him sleep enough during the day and overstimulated him. Babies at that young age cannot stay awake for more than 2 hours straight before needing a good need or getting overtired. A good schedule I think will help. Babies this age average between 15-17 hours of sleep a day. Here is what my son's schedule was when he was that little:
up at 7ish feed
nap from 8:30/9 to 10ish and feed
11:30 feed
nap from 12ish to 2:30ish
2:30 feed
nap from 4 to 5ish
5:30 feed
at 6:30 started sleep routine - calming bath, singing, massage, quiet breastfeed and asleep no later than 7pm
10:30/11 feed (the more baby eats here the better!)
At 5 weeks, its normal for babies to wake up in the middle of the night for a feed. Around 2:30ish and then 5:30ish. Some babies though will only wake up once at 3:30ish and then stretch thru till 7am.
Here is an article that might be helpful.
http://www.kidshealth.org/parent/general/sleep/sleep.html
Good Luck!