It's going to be wobbly, and it might fall over, unless you make a few modifications.
Pegboard MDF will do basically nothing for rigidity. You could maybe scrape by if you put horizontal 2x3s at the top and bottom of the pegboard panels, and a diagonal one across the middle of each. Otherwise, those side panels need to be plywood, at least 3/8" thick.
With this modification, the ridigity of the structure itself looks mostly fine to me, apart from the largest side (which I presume you will have against the wall), which is definitely going to wobble. You do have some brackets, but those and the two horizontal beams are not going to keep it straigtht. Deflection can occur along the length of the boards as well as at the joints (and there's no brackets on those two beams). I would replace them with a piece of plywood that covers the same area as them (or, honestly, a piece of plywood going as far up and down as you can get away with).
The fact that this bed is so narrow means it's going to be harder to keep it stable; if it were wider it'd be harder to put leverage on the structure, but the way it is, even a little bit of lateral motion will change the center of gravity by a lot. If you absolutely can't attach it to a wall...
You mention that the room is only five feet wide (my goodness). In this case, you might be able to use a very simple solution that I've done in small space before -- brace it against the walls. You could put five-foot-long boards at the head and the foot of the bed, that spanned the whole width of the room, and put rubber wedges on either end of both to stabilize them against the wall. Heck, you could do this going the other direction too (70" to 74.5" is only a 2.25" gap on each end).
That said, I don't know how comfortable you are going to be on such a bed, even if it's stable as a rock. I had a phase where I experimented with various compact living arrangements, and I found that anything less than three feet was extremely uncomfortable to sleep on (you have to almost completely raise your body off the mattress to turn while sleeping, for example).