5E seems to have done away with the concept of caster level. Your reading is correct: You get another beam when you hit level 5, even if you're a warlock 1/fighter 4. Likewise, you qualify for thirsting blade at 5th level total.I'm wondering on Eldritch Blast. It says more beams are added as you reach higher levels ... but it never says it has to be warlock levels. Same with Thirsting Blade. It asks for 5th level.
I'm just wondering about this because I'm tempted in taking a dip into paladin at second level, or a fighter dip instead. I'm going with Crossbow Expert, so it's a tough choice.
On the other hand, ability score boosts are now class features rather than a universal benefit, so dipping will delay your access to them.
Also, I highly recommend putting your first level into fighter or paladin, and then going warlock, instead of the other way around. That gives you heavy armor proficiency, plus an extra hit point. (I don't understand why WotC decided it was a good idea to make the order in which you take class levels matter, but if they were going to do it, they should have imposed similar penalties on every class. As it is, you always want to get your fighter/rogue levels first, so you don't miss out on key proficiencies.)
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