I'm not sure which rig you're speaking about, so here goes (again, all info from John Calderone's FDNY Rescue Apparatus):
Rescue 5 was organized May 16, 1948 at 4 Brighton Ave (with L78; I think that's a typo in John's book; should be 14 Brighton Ave), using an open-bed 1941 Ward LaFrance hose wagon [FDNY #290] outfitted with rescue equipment by the shops. During 1957, the members of R5 constructed a closed, rescue-style body on this rig. It remained in service with R5 until Dec 2, 1959, when it became a spare. R5 was then assigned the former R1 (1948 Mack LF/Approved), and ran with that rig until Jun 1, 1962, when R5 was disbanded.
After more than 20 years with no rescue company on SI, R5 was reestablished on Aug 20, 1984, at 1850 Clove Rd (with E160), using a shops-refurbished 1976 Mack R/Hammerly, FDNY #MR7601 (note the new numbering system). This rig had formerly run as R2 (from Jul 76 'til Feb 83, when it became a spare). They ran with this rig until early 1987, when they were assigned their first NEW truck . . . MR8502 . . . a 1985 Mack MR which was not delivered to FDNY until 1987. This rig was reassigned to the spare pool on Apr 18, 1997, when R5 was assigned SR9605, the 1996 HME/Saulsbury rig which was damaged on 9/11, but (I believe) is still in service as a spare. Then later they got their current E1/Saulsbury rig (don't know the exact date or FDNY #, it was after John's book was published ).
Hope this answers your question.