Five yrs is a long time relationship wise. And if this is out of character for him there is some chance of redemption there. The fact he has apologized for it speaks well for him too, so NEVER do.
As to why he doesn't respond, could be a vary of things. Some good, some bad. He doesn't want to face the consequences like your anger or how much he has hurt you. Or he just may not know how to do that, figures you've been hurt enough & the less he says the less chance of causing you any more anguish.
For someone to cheat & betray the person they love means they were not thinking straight & that doesn't always go away magically or automatically once the affair is no longer a secret. The cheater may sincerely be sorry, want to restore the relationship & be willing to put in the needed effort but don't know how to do that. And there may still be some what is called "foggy" thinking going so they can't figure things out very well on their own to make things right the way they deeply want to, if indeed that is the case.
If the cheater stays truly unrepentant & remorseful, the betrayed partner has no other healthy choice than to let them go. If instead the cheater is truly sorry & wants another chance then it's up to them to earn that which then means the betrayed partner has to decide whether to give them that option or not.
If this is the first time he's been busted & he's apologizing, giving him SOME benefit of the doubt isn't a bad thing as long as it doesn't cost you too much. Only you know his history to figure out whether moving immediately without a backward glance or keeping the reconciliation door opened at least a crack to see what he does is best for you. Actions will speak louder than words but not knowing what to do is very different from not being willing to take the proper steps after learning what those are.
Expecting closure from him is a mistake because ultimately that is something only you can give yourself. What he can do, if he's willing, is to give you answers to questions that you want / need. That is often a grueling process after a DDay whether you stay together. The truth there hurts, a lot. But it can also be a very beneficial process for both of you is handled correctly (& that's a big tricky part). Those answers will not necessarily help you but the fact that is willing to face you with the truth is, it can be a mutually healing process so the emotional baggage from this relationship doesn't get unnecessarily dragged onto the next one or to clear the air so restoration of your relationship together is possible.
There is a lot of helpful info regarding that on the SI site (the Surviving Infidelity one I already gave you the link to). In case I didn't mention it already, I would suggest you read the Not Just Friends book to start, Glass has what I consider one of the best affair recovery books in the field, whether you stay together or not it will help you understand betrayal & its effects much better. That's a great starting place & there are also many other sources of help, many free online to put together a great relationship despite the shambles he created with the betrayal.
Amazon.com: Not "Just Friends": Rebuilding Trust and Recovering Your Sanity After Infidelity: Shirley P. Glass, Jean Coppock Staeheli: Books
I wouldn't suggest at all you run after him begging for him to come back, he needs to want that as badly as you do & to help you heal from what he's done. The fact that he cheated once doesn't automatically mean he will keep being a cheater if that's not what he wants for his life. It will be an incredibly hard process & take a long time to get successfully past the betrayal. But it's not impossible & many couples do in fact do exactly that.
The more you know what is going to be required to put the relationship back on track in general & what you need specifically to make it work for you, the better if he wants to work on another chance with you. Another suggestion I have for you is to read the article on how marital therapy can be hazardous to your marriage on the Smart Marriages site, that will help in case you two go to a therapist to weed out one that can make things worse more quickly even if you're not married per se.
William Doherty: How Therapy Can be Hazardous to Your Marital Health
It's a confusing awful time for both, so you don't have to write him off immediately if you are seeing some signs of genuine regret on his part. Without that, there is nothing to work with in order to be able to recreate a good relationship for both of you. For right now, again just take good care of yourself the best you can. That alone is a huge challenge for anyone that's been betrayed right after they've just found out.