In general, Panasonic and Olympus Micro Four Thirds lenses work well across brands, and users report normal autofocus and image quality with no major quirks.

A few practical caveats:

• Stabilization: if the Panasonic lens has optical stabilization, Olympus bodies typically rely on their in-body stabilization instead, so the lens IS is usually unnecessary and best left off.
• Lens corrections/calibration: some automatic lens correction behavior may vary between brands, so cross-brand combinations may not always get every brand-specific correction.
• Weather sealing: if you want a sealed setup on the E-M5, Olympus lenses are the safer match; Panasonic lenses may not offer the same dust/splash protection.

So yes, a Panasonic 25mm on an Olympus OM-D is a fair and reasonable combination, not something likely to cause focusing or compatibility headaches. If your priority is the 25mm focal length, there’s no strong reason to avoid it on an Olympus body.