From D&D 3.5 to 5.0(5E) - 2 - No More Base Attack Bonus (BAB) in 5th Edition Rules

The Base Attack Bonus (BAB) has been replaced by the simpler Proficiency Bonus.  High level rogues will no longer get additional attacks upon reaching certain levels, and may be limited to a single attack their entire career.  But that does not mean the party is over for everyone.  Fighters, for example, can acquire the ability to make two attacks in a round from the "Extra Attack" feat gained at 5th level.  Barbarians also can gain the "Extra Attack" feat at 5th level.  Fighters get another "Extra Attack" at 11th level, but Barbarians do not.

So your character sheets will no longer contain entries like +16/+11/+6/+1 for combat.  The bonus to your attack will be your Proficiency Bonus, which is +3 at 5th level.  Thus a 5th level Rogue will get one attack at +3 with any weapon he is proficient with, and a 5th level Fighter will get two attacks at 5th level, each attack getting his +3 Proficiency bonus as long as he attacks with a weapon he is proficient with.  When a character gets multiple attacks in a round, each attack has the same bonuses to hit.  Strength modifier (or dexterity modifier) + proficiency bonus + the roll on the d20.  If your character attacks using a weapon he is not proficient with, you simply don’t apply the proficiency bonus.  There is no need to deduct anything for lack of proficiency with a weapon.
Are you worried about the lack of attacks for your high level rogue?  Don't be.  The reduced number of attacks is compensated for in other ways in 5.0.