A 5 city axe rush is going to be far too late to be effective even on Monarch. If you have the land to expand to 5 decent cities (I'm assuming a Standard map) Catapult based wars are far more hammer effective. If you have a neighbour that is close enough to axe rush, aim for 3 cities MAX before you rush.
Courthouses suck. Don't build them until your cities are costing 8+ gpt in maintenance. Build Wealth/Research instead. (Currency is a far, far better economy tech than COL).
As far as specific advice regarding what you are doing wrong, it's hard to say without having a look at some save games.
Next time you start a game, upload the 4000BC save + saves from `1k BC and 1 AD. Most advice is specific to the situation you find yourself in wrt to terrain, leader, civ and neighbours.