Let's compare RAW builds to a multiclass build with your house rule:
RAW 3 Berserker Barbarian / 2 Monk: gets 1 attack action and as a bonus action either;
- 2 unarmed strikes from Flurry of Blows (For 1 Ki)
- 1 melee weapon attack from Frenzy (While Raged)
- 1 unarmed strike from Martial Arts
Assuming combat lasts for 1 minute, rage is active, all attacks hit with Quarterstaff for 4+3 mod+2 rage= 9 damage and all unarmed strikes hit for 2+3 mod +2 rage= 7 damage and all resources are used optimally; This character can deal:
Round 1 & 2 : 9 + 7 + 7 = 23 damage per round (46 damage total)
Round 3 to 10: 9 + 9 = 18 damage per round (144 damage total)
Total Damage after 10 rounds: 190 damage
3 BERSERKER / 2 MONK with you house rule:
with an extra attack at level 5 in comparison will deal:
Round 1 & 2: 9 + 9 + 7 + 7 = 32 damage per round (64 damage total)
Round 3 to 10: 9 + 9 + 9 = 27 damage per round (216 damage total)
Total Damage after 10 rounds: 280 damage
We can observe that the house rule boosts damage by ~47%. But how does that compare to pure RAW builds?
Compared against other RAW Builds we can see that the RAW Multiclass Build loses a lot of damage:
RAW 5 Berserker Barbarian Quarter-Staff: gets 2 attack action and as a bonus action either;
- 1 melee weapon attack from Frenzy (While Raged)
Assuming combat lasts for 1 minute, rage is active, all attacks hit with *Quarterstaff for 4+4 mod+2 rage= 10 damage* and all resources are used optimally; This character can deal:
Round 1 to 10 : 10 + 10 + 10 = 30 damage per round (300 damage total)
Total Damage after 10 rounds: 300 damage
RAW 5 Berserker Barbarian Great Sword: gets 2 attack action and as a bonus action either;
- 1 melee weapon attack from Frenzy (While Raged)
Assuming combat lasts for 1 minute, rage is active, all attacks hit with *Great Sword for 6+4 mod+2 rage= 12 damage* and all resources are used optimally; This character can deal:
Round 1 to 10 : 12 + 12 + 12 = 36 damage per round (360 damage total)
Total Damage after 10 rounds: 360 damage
RAW 5 Berserker Barbarian Great Sword and GWM Feat: gets 2 attack action and as a bonus action either;
- 1 melee weapon attack from Frenzy (While Raged)
Assuming combat lasts for 1 minute, rage is active, all attacks hit with *Great Sword for 6+3 mod+2 rage + 10 feat bonus= 21 damage* and all resources are used optimally; This character can deal:
Round 1 to 10 : 21 + 21 + 21 = 63 damage per round (630 damage total)
Total Damage after 10 rounds: 630 damage
RAW 5 Monk (Drunk Master): gets 2 attack action and as a bonus action either;
- 2 unarmed strikes from Flurry of Blows (For 1 Ki)
- 1 unarmed strike from Martial Arts
Assuming combat lasts for 1 minute, all attacks hit with *Quarterstaff for 4+4 mod= 8 damage* and all *unarmed strikes hit for 3+4 mod = 7 damage* and all resources are used optimally; This character can deal:
Round 1 to 5 : 8 + 8 + 7 + 7 = 30 damage per round (150 damage total)
Round 6 to 10 : 8 + 8 + 7 = 23 damage per round (115 damage total)
Total Damage after 10 rounds: 265 damage
In conclusion:
Allowing your Player to get an extra attack at level 5 for this specific multiclass build may give that player a ~47% boost in damage over the course of 10 rounds. Of course, this was just a quick example build that I used for comparison. Greater damage may be achieved with a more optimised build.
In actual play, the damage will probably be less due to missed attacks, unoptimal actions, losing rage etc...
Compared to Pure Monk 5 builds doing damage over 10 rounds, the damage increase is still present but not as significant. Pure Barb significantly outpaces damage of other builds, especially with Great Weapon Master Feat. Of course, a multi-class build has more access to class feats that pure builds do not have.
RAW 3/2 loses damage in exchange for:
- Rage
- Unarmoured Defense
- Reckless Attack (Attack with Advantage for disadv. when attacked)
- Danger Sense (Adv. Dex Save)
- Frenzy
- Martial Arts
- Ki
- Unarmoured Movement (+10 ft speed)
Whether this mixture is worth the damage reduction or not is up to you. Personally, I think that an increase in ~47% damage over RAW build is far too generous but this multiclass has a huge damage output reduction compared to pure builds.
Another interesting question to ask is if this damage gap closes once the RAW multiclass gains extra attack at level 7, 8 or 9 compared to other pure RAW builds at the same level. If it does the player may feel rewarded for putting up with a weaker start as his or her character starts coming into its own.
If the extra attack is awarded early, the later levels might feel stagnant as his or her power curve is flattened.
Perhaps allowing Ki and Rage resources to be combined would be a good compromise rather than an early free extra attack?