Thanks so much for your kind words about the Moms Panel, Sabrina; we appreciate it! As for your question, you're cutting it close.
Mickey's Jammin' Jungle Parade starts at 3:45 and lasts about fifteen minutes. I can also tell you that the walkways get especially congested at Animal Kingdom during the parade, meaning it's a bit harder to make a quick exit. Assuming you can get out relatively quickly, though, (by 4:10, let's say) that leaves you just over an hour to get to the Beach Club. You could luck out and have a short wait for the bus, but then again, you might have to wait fifteen or twenty minutes. Let's say that puts us at 4:30. The actual trip to the Beach Club via bus should take you about thirty minutes. We're at five o'clock now. Assuming you really high-tail it from the bus stop at the Beach Club into the resort and over to Cape May, you technically could make it. It's a bit close for comfort, but if you're up for the challenge, I say that yes, you probably
could make it. No lolly-gagging though! Enjoy your trip.