It seems like the same lights that I used in P4 aren't producing any shadows in P5. Are there light settings specific to P5?

In p5 you have to set ray trace shadows in the light properties box, p4 lights should work in p5 ok.

Actually, you can leave the light property set to "Depth map shadows" if you want. With either depth map or ray traced shadows, make sure "Cast shadows" is selected in the Render Options menu, plus "Raytracing on" if you set the light properties to Ray Trace shadows as suggested by xantor.

Poseur is dead on. The lights in P4 and P5 are the same. They added the ray tracing capability. In the render settings, when using firefly, you must select cast shadows. I also recommend you uncheck smooth polygons and texture filtering unless you have a specific use for them. lastly, should you use any of the ray traced lighting shaders, you will need to have ray trace checked in render settings to get their full effect -- even if you have no ray traced lights.