Going with more gears on the cluster doesn't necessarily give you a better climbing.

It usually gives you more gears in between.

You can get a 5 speed cluster that is 14-34, or a 10 speed 11-23, and the 5 speed will have a lower gear, assuming you have a derailleur that will handle it.

Even a common 14-28 5 speed will climb better than the 11-23.