I have been punching air with 5 pound weights in my hands but is there a better way to built power and speed?

Power and speed are often what people seek.

Different amounts of muscle tension produce different amounts of each.

You do not have to use weights to produce more tension in a muscle, even while moving.

Some people find less tension in a muscle can be useful.

You should vary your workout, and vary if you use a weight at all, at times.

But mostly importantly do not overdo, do not try to use too much weight,
Because it is better to be safe and not injure yourself.

If you must use a weight, change what you do with a weight in your hand,
Do other exercises besides just punching, and do punching at different angles.

By changing how the muscles must work and what part of the body works ,
You get used to doing something, and then muscle confusion is done to get more gain.
So change how fast and how slowly you punch, your muscles will respond differently.

Overall gain is useful for control, and size of slow twitch muscle, and the other with fast twitch.

I agree, Eawoodall have you ever studied traditional African wrestling in Nigeria or west Afirca in general?