I think I see your point. The 5th floor is 4 stories above the level of exit discharge (since the 1st floor is on the level of the exit discharge) so a 4 story building would not require an elevator, per Chapter 10. If you are designing such a building, I would call the building official to confirm this is the jurisdictions interpretation before you apply for a permit.
Assuming a new building, ADAAG would require:
4.1.3 Accessible Buildings: New Construction.
(5)One passenger elevator complying with 4.10 shall serve each level, including mezzanines, in all multi-story buildings and facilities unless exempted below. If more than one elevator is provided, each passenger elevator shall comply with 4.10.
EXCEPTION 1: Elevators are not required in:
(a) private facilities that are less than three stories or that have less than 3000 square feet per story unless the building is a shopping center, a shopping mall, or the professional office of a health care provider, or another type of facility as determined by the Attorney General; or
(b) public facilities that are less than three stories and that are not open to the general public if the story above or below the accessible ground floor houses no more than five persons and is less than 500 square feet. Examples may include, but are not limited to, drawbridge towers and boat traffic towers, lock and dam control stations, and train dispatching towers.
The elevator exemptions set forth in paragraphs (a) and (b) do not obviate or limit in any way the obligation to comply with the other accessibility requirements established in section 4.1.3. For example, floors above or below the accessible ground floor must meet the requirements of this section except for elevator service. If toilet or bathing facilities are provided on a level not served by an elevator, then toilet or bathing facilities must be provided on the accessible ground floor. In new construction, if a building or facility is eligible for exemption but a passenger elevator is nonetheless planned, that elevator shall meet the requirements of 4.10 and shall serve each level in the building. A passenger elevator that provides service from a garage to only one level of a building or facility is not required to serve other levels.
EXCEPTION 2: Elevator pits, elevator penthouses, mechanical rooms, piping or equipment catwalks are exempted from this requirement.
EXCEPTION 3: Accessible ramps complying with 4.8 may be used in lieu of an elevator.
EXCEPTION 4: Platform lifts (wheelchair lifts) complying with 4.11 of this guideline and applicable State or local codes may be used in lieu of an elevator only under the following conditions:
(a) To provide an accessible route to a performing area in an assembly occupancy.
(b) To comply with the wheelchair viewing position line-of- sight and dispersion requirements of 4.33.3.
(c) To provide access to incidental occupiable spaces and rooms which are not open to the general public and which house no more than five persons, including but not limited to equipment control rooms and projection booths.
(d) To provide access where existing site constraints or other constraints make use of a ramp or an elevator infeasible.
(e) To provide access to raised judges' benches, clerks' stations, speakers' platforms, jury boxes and witness stands or to depressed areas such as the well of a court.
(f) To provide access to player seating areas serving an area of sport activity. Appendix Note
EXCEPTION 5: Elevators located in air traffic control towers are not required to serve the cab and the floor immediately below the cab.
Don Phillips