Sorry to interrupt you lovebirds, but how does base attack progression work in 5th edition ?
I assume its different, given that +3 on a weapon is considered a large bonus.
5E extremely simplifies bonuses and progressions: you no longer have an attack bonus and various saves bonuses, instead you have a single bonus (called proficiency) that goes from +2 at level 1 to a maximum of +6 at level 17. Everytime you roll to do something, if you are "proficient" in wathever you are trying to do, you add your proficiency bonus to the relevant ability bonus for that task.
Characters' abilities are capped at 20 (which gives a +5 bonus) and there are very few ways of getting higher scores (very few means just two or three in the entire game).
Another important thing to know is that there are very few ways to get a bonus on your roll (a couple of spells and class features), so usually your maximum bonus on any given roll can't exceed +11.