Could it be the RX-7 LM Race Car? Or is it a regular RX-7? Most of them look the same with small changes.
It seems as though all GT5 RX-7 cars were in GT4. As far as spoilers go, most of these have multiple versions so they look alike. The only one with a noticeable "large" spoiler is the LM Race Car. Most of them do have a spoiler, but they have a small one unless replaced with a larger one.
GT5 RX-7 cars:
Mazda RX-7 GT-LIMITED (FC, J) '85
Mazda RX-7 GT-X (FC) '90
Mazda RX-7 GT-X (FC, J) '90
Mazda RX-7 LM Race Car
Mazda RX-7 Spirit R Type A (FD) '02
Mazda RX-7 Type R (FD, J) '91
Mazda RX-7 Type R (FD, J) '93
Mazda RX-7 Type R Bathurst R (FD) '01
Mazda RX-7 Type RS (FD) '98
Mazda RX-7 Type RS (FD) '00
Mazda RX-7 Type RS (FD, J) '96
Mazda RX-7 Type R-S (FD, J) '95
Mazda RX-7 Type RS-R (FD) '97
Mazda RX-7 Type RZ (FD) '00
Mazda RX-7 Type RZ (FD, J) '92
Mazda RX-7 Type RZ (FD, J) '93
Mazda RX-7 Type RZ (FD, J) '95
Mazda RX-7 Type RZ (FD, J) '96
GT4 RX-7 Cars:
Mazda RX-7 GT-Limited (FC,J) ('85)
Mazda RX-7 GT-X (FC) ('90)
Mazda RX-7 Infini III (FC) ('90)
Mazda RX-7 Type R (FD, J) ('91)
Mazda RX-7 Type RZ (FD, J) ('92)
Mazda RX-7 Type R (FD, J) ('93)
Mazda RX-7 Type RZ (FD, J) ('93)
Mazda RX-7 Type R-S (FD, J) ('95)
Mazda RX-7 Type RZ (FD, J) ('95)
Mazda RX-7 Type RS (FD, J) ('96)
Mazda RX-7 Type RZ (FD) ('96)
Mazda RX-7 Type RS-R (FD) ('97)
Mazda RX-7 Type RS (FD) ('98)
Mazda RX-7 Type RS (FD) ('00)
Mazda RX-7 Type RZ (FD) ('00)
Mazda RX-7 LM Edition ('01)
Mazda RX-7 Type R Bathurst R (FD) ('01)
Mazda RX-7 SPIRIT R Type A (FD) ('02)