Why not just buy a wood wheel (which, by the way, since Egyptian times, most wood wheels have six or more spokes. (I did see a picture of a four spoke on one though)
CNC cut metal custom car wheels are a different ballgame.
You can Google five spoke wheel to check, however. Will a five spoke WOOD wheel hold up to weighted rolling stresses? What is the size of the hub? What is the size of the wheel rim inside diameter? If you are going to mortise the spokes remember that in addition to additional length the shoulders will need to match the curve of the outside of the hub, and the inside of the wheel rim. Wheelwrights use a heated metal rim with rapid cooling to shrink the rim and tighten the already tight wood spokes from the outside in. Elm has been a favorite for the stresses on the hub.
You can, of course drill and insert the spokes, but will they stay where you put them as with only five spokes they will have way more stress than say a Windsor chair back.
Lastly, for me, you could make a Carnival single piece five spoke wheel (maybe double up the thickness) and cut out the portions between the hub and wide rim.
No matter how you do it you will need a metal bushing at the axel to keep wear down at the critical connection point. With all the concerns, if you're committed, go for it,