Can GTA 5 Run on PlayStation 2?

Absolutely not.

• Hardware Gap: PS2 = 299 MHz EE + 47.6 MHz VU1 + 32 MB RAM. GTA V requires ~1.5 GHz x86, 8 GB RAM, 2 GB VRAM, Shader Model 5.0.
• Release Timeline: PS2 discontinued 2013; GTA V launched 2013 (PS3/360), 2014 (PS4/XB1), 2015 (PC).
• Engine: RAGE (Rockstar Advanced Game Engine) — x86/PS3 Cell/PS4 GCN only. No MIPS/EE backend.

GTA on PS2

• GTA III, Vice City, San Andreas — native, excellent.
• GTA Liberty City Stories / Vice City Stories — PSP ports, also on PS2 (slightly downgraded).

For open-world crime on PS2: San Andreas remains the peak. For GTA V: need PS3/PS4/PS5, Xbox 360/One/Series, or PC.