Well, we had problems getting ds to go to sleep so we tried controlled comforting which is an Aussie modified version of controlled crying for babies under 6 months. (You'll find it if you do a google search.) Although quite stressful for all concerned, it meant that the poor little thing knew that when he was turned on his side and had his back patted, it was time to sleep. Once he had that association, I could use it in the night to get him back to sleep. (Once he had learnt to settle himself, we didn't need to do this any more.) I think I reinforced his night-time waking because he ALWAYS got fed immediately 'cos I didn't want DH to be disturbed. When I started doing this in the night (which led to a week or two of more disturbed sleep for DH), it could take a while (up to 20 minutes on one occasion) to get him back to sleep, but generally didn't take too long. Guess you could give it a go if it appeals - the good thing about it is that you do comfort the baby whilst waiting for him/her to go back to sleep, rather than just leaving them to cry.
Also, I kept a mental note of how long he went between feeds. For example, once he had gone for 3.5 hours between feeds, if he woke up less than 3.5 hours from his last feed, I would try to get him to go back to sleep rather than feeding him. Amazingly, he would usually go back to sleep for an hour or so, so the times between feeds lengthened out quite quickly. But you do have to take a view fairly quickly (based on time since the last feed) whether they are so hungry that they simply won't go back to sleep...
It did take a couple of weeks of disturbed nights sleep until he started going for longer stretches of time, but it was worth it. Once ds realised he wasn't getting a cuddle and food when he woke up, he had much less of an incentive to wake.
The other thing you could try is stretching the time between night feeds out gradually using cold boiled water. I think this creates a cycle where they are hungrier in the day so they feed more and the knock-on effect is that they are less hungry during the night - in theory...
Mind you, none of the above has yet sorted out the 5am start to our days!!