I saw someone's iphone5 whatsapp notification pop up with only the whatsapp badge and the word "message" but I can't figure out how to do that on my iphone5
On your iPhone go to Settings > Notifications > WhatsApp > scroll down and you'll see "Show Previews" > And change that.
Also in WhatsApp settings. Click on Notifications. The toggle "Show Preview" off.
That should only show the senders name and not the context of the message.
You can also turn of show on lock screen for WhatsApp in iPhone notification settings for added privacy.