I had sex with my wife after morning suhoor at 5:30am. It was the feeling that cause it, it was not intentional.
Can I still proceed with my fasting? And what else is implication of this?
First of all nobody expect your wife and you could judge your intentions. But all i can do is to give you a guideline that might help you to find the correct ruling for your case.
Here are the most common and relevant sources which are the basis to find a ruling:
From this we can conclude the following:
As you only gave as a timing 5:30 AM and we don't know where you are we don't know whether this intercourse happened before fajr/dawn or afterwards:
If it happens before there's nothing to do -expect performing ghusl to be able to pray- as it was allowed, if not -and this is what I assume- you (both) committed a major sin, especially if you were aware that you are fasting or of this being haram at any moment of this act. In that case you'll have to perform the big kafara (please read my later checklist). But first of all you both need to repent from this sin no matter if you were aware of the decay or sin you committed or not, as you later recalled that you should be fasting. Now lets see what kind of expiation should be performed:
So: Each of you must ask himself the following:
Now finally to your question: can i still proceeding my fasting?
Yes you even should, read for example this fatwa.
See also this fatwa (in Arabic) of the Saudi Fatwa council which concluded that the wife must perform the big kafara only because she recalled or reminded her husband later about the fact that this was Ramadan or they were fasting without knowing the ruling, which is a clear contradiction to this fatwa.
On the other hand no matter what happened during your fasts in Ramadan I've never heard or read a fatwa of a scholar saying or recommending if one breaks his fast no matter if it was by intention or not to eat. As in case you made it forgetfully your fast is valid in any other case -except you couldn't fast any more for example for health reasons or you feared you would die if you don't drink or eat- you should go ahead fasting to show Allah that you repent from the previous committed sin. So you shouldn't commit a new sin by breaking your fast -this time for sure- intentionally!
And Allah knows best!