If it's only been 5 months and you haven't seen him in a month and a half despite living only 10 minutes apart, it seems like you're effectively broken up. But just so both of you are on the same page, it would be good to have a breakup talk.

You don't have to see him in person. In this case, phone might be easiest. Message him something like "hey, can we talk tonight?" and set up a time. If a call or setting up a time isn't feasible, then just do it over text.

You don't have to give a reason. You can say that you really enjoyed your time together over the summer but just aren't feeling the spark anymore, so you think it's best if you break up.

If he begs you to stay and says he'll change, you can say that you've already been turned off by his recent behavior, and continuing the relationship is not an option. Or, if this situation arises and you'd prefer to give him another chance, be really clear about how you felt about how you were treated and what you would want to change. Give yourself an internal timeline. If there aren't noticeable changes in 1 month (or 1 week or 2 month or whatever) then you leave.

You absolutely shouldn't blame yourself. It sounds like it just fizzled out, and sometimes that's not anybody's fault. Often two people aren't always compatible, but it takes some time to figure that out. But once you figure that out, it's best to leave so that you're open and available for new opportunities or relationships.

Best time of day is when you know you'll both be available. Don't message him before you're both about to start a full day of classes (or work, or travel, or whatever) because it might make him less likely to respond, or force you both to go through the whole day knowing that "the talk" is coming and kind of dreading it.

You also don't have to give him a laundry list of all the ways he's failed. For both your sakes, just keep it simple so it's over quickly and you can begin the process of moving on. Save the lis of grievances to vent about with a friend.