I don't think there is an average age for a lesson horse; it really depends on the specific animal. I've ridden 20+ year old horses who would make abysmal lesson mounts, and 4-5 year olds that could easily pack a rank beginner safely and still teach them something.
A younger horse can generally be expected to be a bit more flighty, just because they don't have years of "life experience" behind them, but that's a very
general statement. Sometimes younger horses are less forgiving of rider error, and hence a bit harder for a beginner or re-learner to ride, simply because they are used to more experienced riders or trainers who can be very correct and accurate with their position and aids. Honestly, sometimes those less forgiving horses teach us the most, because they force us to do things the right way or they won't give us the result we want. There's no reason why a 5 year old cannot be precocious and have the right experience to be a good lesson mount. I wouldn't worry about it unless the horse gives you a reason to doubt him.