With younger kids it is more important for you to instill a love of music, not necessarily just to teach them like you would someone older. I have had hundreds of 5 year old students, who later became, 6, 7, 8, 9 year old students. It's such a great feeling getting to know someone musically at such a young age! I have even had 4 year old students. I think they are the most fun because they really are the easiest to entertain, and if you tell them they did a good job, they appreciate it MUCH more than older students. My "Wow!! That was SO amazing!!" doesn't quite sound as over-blown as it would to an adult. I always overly compliment my younger students to help them feel more secure and more excited about playing. This also helps them pay attention.
I also like to play chord progressions and let them ad lib in C position. I will switch to things like "bouncy" and "smooth" and "super loud" and "super quiet" and as I change my playing, he/she changes to match.
I also incorporate CDs with my lessons. There is a series called "Proggressive" from Australia that is excellent for young beginners. It goes throught the notes one at a time. The first song is just "C" over and over, but with the CD it sounds really neat. Also, it teaches the left hand in regular C position. I don't know about the other teachers, but teaching a young child middle C position, then changing it, is just confusing for them and annoying for me.
Composition can also be really fun for 5 year olds, and it can take up TONS of lesson time. I teach mine to draw all the notes and symbols. Then, I help them come up with a melody, and they draw it out themselves in pencil. Then I go through and clean up their mess so they can practice it. At the school I used to work at, I would print out copies of their music using Encore, a music writing program, but I have yet to purchase a program like that for my independent students.
You may wonder, how can a 5 year old write their own music? In order to assist them with their composition, I divide their music into 8 or 16 measures, and let each 4 measures begin and end on C. This way, no matter what they come up with, it'll sound somewhat decent. I let them fiddle around with melodies, and I kind of guide them on what sounds good and what doesn't. Then we decide which notes are quarter, and which are half, and how many can fit in each measure. It's fun, it's time consuming, and at the end the student has a song that they can rightfully claim as their own (even if I did do most of it myself.) If they are really creative, they can even add words! I sing about a playground swing with one of my 5 year olds at the beginning of almost every lesson. She loves it!
I don't think you should give up on this kid, in any way. His father AND his brother play, and in my experience that's almost a guaranteed student for life (or till they leave for college.)
This along with the games that have already been suggested should be plenty to fill up your lessons! I hope this was helpful.
Take care,
cj