I was playing with the idea of a charging Barbarian in 5e. What I would like to know is if there is anything within this build that would not work.

Step 1: Choose Variant Human as your race. This would mainly be for the bonus feat you get from it, allowing you to pick up the Charger feat (PHB p. 165):

When you use your action to Dash, you can use a bonus action to make one melee weapon attack or to shove a creature.

If you move at least 10 feet in a straight line immediately before taking this bonus action, you either gain a +5 bonus to the attack's damage roll (if you chose to make a melee attack and hit) or push the target up to 10 feet away from you (if you chose to shove and you succeed).

Step 2: Pick a maul and short bow as your weapons. The maul does 2d6(+Str) bludgeoning damage; the shortbow does 1d6(+Dex) piercing damage.

Step 3: Take 4 levels in Barbarian. For your primal path at level 3, choose Path of the Zealot (Xanathar's Guide to Everything, p. 11), which gives you the Divine Fury feature:

Starting when you choose this path at 3rd level, you can channel divine fury into your weapon strikes. While you’re raging, the first creature you hit on each of your turns with a weapon attack takes extra damage equal to 1d6 + half your barbarian level. The extra damage is necrotic or radiant; you choose the type of damage when you gain this feature.

Step 4: At level 4, take the Great Weapon Master feat (PHB p. 167):

You've learned to put the weight of a weapon to your advantage, letting its momentum empower your strikes. You gain the following benefits:

• On your turn, when you score a critical hit with a melee weapon or
  reduce a creature to 0 hit points with one, you can make one melee
  weapon attack as a bonus action.
• Before you make a melee attack with a heavy weapon that you are
  proficient with, you can choose to take a -5 penalty to the attack
  roll. If the attack hits, you add +10 to the attack's damage.

If my understanding of the rules is correct, on my first turn I would be able to rage as a bonus action, and shoot my bow to maintain it. Then on subsequent turns, I would be able to "charge" by using my action to Dash 10 ft in a straight line, giving me a bonus action attack with +5 damage.

I can choose to make that a Reckless Attack, granting myself advantage on the attack (and giving enemies advantage on attacks against me):

Starting at 2nd level, you can throw aside all concern for defense to attack with fierce desperation. When you make your first attack on your turn, you can decide to attack recklessly. Doing so gives you advantage on melee weapon attack rolls using Strength during this turn, but attack rolls against you have advantage until your next turn.

Next, I choose to give myself -5 to the attack roll and +10 to damage on a hit, thanks to GWM. Finally, the Zealot Barbarian path would add 1d6 + 2 to the damage of the attack if it hits, and Rage would add an additional 2 damage to the hit.

This means that at level 4, every round, I could move more than 10 feet into combat, then make an attack with -5 to the attack roll but advantage on the roll, and do a total of 3d6+19+Str damage? Are my calculations correct?