With my repairs, I always try to start and end the repair right down the center of a joist, so the new wood and existing wood has something to be nailed own to. When that is not possible, up against a wall for instance, then I have to frame in blocking to be that joist. The cuts going the other way will be spanning joists. There must be blocking under this cut. When fastening in the new wood, remember to re-nail/screw the edge of the existng subfloor to attach it to the joists and blocking as well. Nail pattern is 4"oc around the perimeter and 6"-8" in the field. I use PL adhesive with the screws to ensure no squeaks.
I would go with 3/4" plywood for the repair. 5/8" plywood is a nominal thickness. Actual thickness is 19/32". While this is closer to the thickness of 5/8" particle board, which actually is 5/8" thick, the 19/32" is a bit soft and spongy (I do believe 19/32" is legal with 16" oc joists though). Going to 3/4" (23/32" actual), you should end up with a lip on the edge of the repair because of the thicker plywood. This edge is reduced by floating out the difference with floor compound, to the point where the change is unnoticeable.
Today is PERFECT!
All information and advice given is for entertainment and informational purposes only. The person doing the work is solely responsible to insure that their work complies with their local building code and OSHA safety regulations.