Hello, I am finishing a basement that will consist of a large play room and office.
The play room is 20X30 and the office is 11X12.

Questions:

Can I run all of the receptacles for both rooms then at the end have 5 recessed lighting fixtures? I would guess about 20ish something receptacles.

I am using a 15 Amp breaker and 14-2 Romex wire.

See Attachment.

Even though there is no maximum amount of general purpose lighting outlets on a residential circuit, and what you propose is allowed by code, I do not think you will be pleased with it's performance.

I would at least have the office on a circuit separate from the family room.

If you plan to have computer, printer, electric heat, de-humidifier, large screen TV, or anything similar, I would suggest another circuit or two, for those large, critical, or high energy appliances.

Also, looks like you need an outlet in the lower right corner of the family room, to the right of the panel. Code reads, as a maximum spacing, that "receptacles shall be installed so that no point measured horizontally along the floor line in any wall space is more than 6 feet from a receptacle outlet."

This means, starting at an opening,such as a entry door, measure from the door 6 feet, place the first outlet, and then space the next outlets no more than 12 feet apart. They can be closer, as you see fit, but no more than 12 feet. And any continuous wall space two feet or more needs an outlet.