What are the best ways to play with my 5-month-old?

Have fun! At this age, babies are very social, and enjoy responding and commenting with babbling. Many babies enjoy interacting with a "baby" in a mirror. They may enjoy looking for a hidden object over and over. Be careful to select toys that require baby to be active, as opposed to one that exposes a moving circus and then explodes all on its own after the parent touches a single button.
Make the baby happy. Three to six month old babies like to play. Activities that make a baby smile are good to continue, such as holding/cuddling the baby, gently teasing the baby with a stuffed toy, singing a song to the baby, talking to the baby, a brief baby massage, playing peek-a-boo, etc.