Don't confuse ASME IX F-numbers with A-Numbers or P-Numbers.  E309L is assigned ASME IX F-No. 5 and A-No. 8.  E9018-B3 is F-No. 4 and A-No. 4.  2.25Cr1Mo base metal is assigned P-No. 5A.  The 300 series stainless steel base metals are assigned P-No. 8.

F-Numbers are groupings of filler metals or electrodes with similar welding characteristics.
A-Numbers are groupings of similar weld metal alloy chemistries.
P-Numbers are groupings of base metals with similar weldability, chemistry and strength level.

From ASME section IX (pages 128 & 129)

QW-430 F-NUMBERS
QW-431 General
The following F-Numbers grouping of electrodes and welding rods in table QW-432 is
based essentially on their usability characteristic, which fundamentally determine the ability of
welders to make satisfactory welds with a given filler metal. This grouping is made to reduce the
number of welding procedure and performance qualifications, where this can logically be done.
The grouping does not imply that base metals or filler metals within a group may be
indiscriminately substituted for a metal that was used in the qualification test without
consideration of the compatibility of the base and filler metals from the standpoint of
metallurgical properties, postweld heat treatment design and service requirements, and
mechanical properties.

F-Numbers from page 129 ASME
5 SFA-5.4 austenitic and duplex EXXX(X)-15 . . .
5 SFA-5.4 austenitic and duplex EXXX(X)-16 . . .
5 SFA-5.4 austenitic and duplex EXXX(X)-17

We must make sure that the welder is qualified with or without backing.

The answer to your question is "YES", a welder qualifed with a F5 electrode is only qualified for F5 electrodes per ASME Section IX.

Best regards - Al