Hi and welcome to my Caitlyn build. I call it pentakill Caitlyn because, in my opinion this is the best possible Caitlyn build which ive had penta's with, and so should you. It is a balanced build, combining near 100% crit, with considerably tankiness damage and lifesteal. This build can also solo Baron.

You start with a Dorans Blade, last hit until you can afford a Pickaxe which is never too long as a BF sword for first item often leads to a very slow start. When you can afford a Zeal go back and get one, i usually get a Vampiric Scepter at this point too. After i'll get a BF sword, and usually can afford a Dagger at the same time. Finish the infinity edge, after that your first Phantom Dancer. Next i like to get either a Phage or a Giants belt to start that Frozen Hammer. Once thats done, grab another Phantom Dancer and finish with a bloodthirster.

+ Damage
+ Survivability
+ Utility with long range slow

- Weaker against high armour targets.

Frozen Hammer with near 100% crit and a bloodthirster makes you pretty much unkillable, and you dont even have to get into the battle. Cait's range makes Frozen Hammer super effecive, and combined with the Bloodthirser and near 100% crit, you are a nemises to absolutely anyone.