You definitely need to open up that joystick and take pictures of the stick area and PCB. There could be a crack or line tear somewhere but nobody will know until you open it up!
I’ve owned and modded some T5’s in the past and they’re roughly equal to a standard HRAP 2/3 in weight even though the parts Hori uses in the T5’s are far inferior to the HRAP 3’s (especially the more limited HRAP 3 SA models). The Hori T5 is really closer in configuration to an HRAP 1 – same button layout minues the turbo panel the HRAP 1 has. T5’s are still great sticks for introductory mod lessons and easy to bring up to HRAP Pro-level if you follow the mod guides and install arcade parts. You don’t even have to pitch the PCB, either! Very easy to mod that PCB and continue using it as a PS2-native joystick and on the PS3 with compatible adaptors. You really don’t to get rid of the PCB unless it gets irreparably broken or you absolutely want a multi-console joystick. In that case, your options are MC Cthulu (for everything but an easy X360 option) or the PS360+ (more difficult option; also no telling when retro system compatibility will be available; the MCC is the better choice for everything but 360 compatibility out of the box).
Minor technical point – Hori never made an HRAP joystick for the PS1. All HRAP 1’s and 2’s were made for the PS2, and HRAP 3’s for the PS3. Difference this generation is that Hori broke with the traditional HRAP case (the same one used for the T5 stick) and has introduced 4 new deluxe cases to date in the past 2.5 years – the HRAP V3/VX, the limited edition HRAP VLX, the “Soul Calibur V/Gundam Extreme” case, and the Fighting Edge case (which looks to be a highly modified HRAP V3 with Hori parts and LED’s with some neat features built in).
No word yet that Hori has officially dropped the traditional HRAP case because they seem to release occasional variant limited edition HRAP’s that still use the design like the recent Tekken Tag Tournament Prologue HRAP 3.