Is There a "Petz 5" Game?

No. There is no game titled "Petz 5." The series numbering skipped from Petz 4 to spin-offs and reboots.

Mainline Petz Series (Ubisoft)

• Petz: Dogz 2 & Catz 2 (DS, 2007) — often called "Petz 3" colloquially.
• Petz: Dogz 2 & Catz 2 (Wii/PC) — separate 3D versions.
• Petz: Hamsterz 2, Horsez, Bunnyz, etc. — standalone sub-series.
• Petz: My Petz (DS, 2010) — unified multi-pet simulator (dogs, cats, horses, dinosaurs).
• Petz Fantasy (3DS, 2011) — mythical creatures (unicorns, dragons).

Modern Equivalent

Little Friends: Dogs & Cats (Switch, 2019) — spiritual successor by Imagineer/Ubisoft.

If you recall a specific pet type or platform, I can pinpoint the exact title.