Very Rare
There are a lot of similarities of this staff to staves like the Staff of Fire (Very Rare) and that of the Staff of Power (Very Rare).
The Staff of Power provides the +2 to attack/damage/Spell rolls that yours does as well as additional casting capabilities that are quite powerful. The Staff of Fire doesn't have the +2, but it does have a similar option of delivering additional damage on a strike.
The next level up would be a Legendary staff like the Staff of the Magi. The biggest uptick in power here is in the number of charges (50) and breadth of available casting options. Yours does not have this.
Comparing the Very Rare to Legendary options, yours fits quite nicely in Very Rare.
Lowering the DC
I'm not sure if lowering the DC would be the impactful, but you may want to consider dropping the built-in DC and use the spellcaster's DC instead like the standard magical staves of this level do.
Either effect is going to have repercussions.
Exact balance can be hard to determine
The two effects can be reduced to damage per round, but that's really not going to tell you much about how it's going to affect your characters in your game.
Basically, the character will be getting a magic item. In campaigns with a lot of magic items the addition probably isn't that significant. In a campaign where at level 5 there are no or few magic items, the effect will be greater.
The breath weapon is likely more powerful
For many characters the breath weapon is going to be more powerful, just because it does more damage. However, for a martial character, larger weapons doing an additional 1d4 is significant, and for many characters advantage on strength checks and saving throws would be, well, advantageous.
You need to deal with the issue of a breath weapon as a bonus action
Of significant issue is that the potion of fire breath says you can use a bonus action to breathe the fire. This is a significant feature, if permanent. Some DM discretion is called for here. A permanent breath weapon bonus action is significant, and as a DM I would pretty likely rule that out as a hard no, not happening.
Although, after looking at it, you may find it's not significantly overpowered even as a bonus action. Or perhaps the player is really keen on the bonus action feature. If you want to allow the bonus action but limit it, you could make it usable 3 times daily, which is reasonable based on the original potion. That way they'd get to have it as a bonus action, but there would be some limits.
Other than that, the breath weapon is not going to be outrageously unbalancing
In the end, depending on your game, the breath weapon is probably not going to be outrageously unbalancing (assuming you account for the bonus action), any more than many magic items. After all, the damage at an average of 14 on a failed save isn't extreme, especially since it doesn't scale with level, and depending on how you rule, it costs an action or bonus action that the character can't be otherwise using.
Take the player into account
To me, what the player wants is probably pretty important, and so you might consider discussing with them, so that you can figure out the most fun option.
Good luck!
Best Answer
Common is probably the appropriate Rarity for this item
This object has one advantage over a Potion of Healing, and two Disadvantages over a Potion of Healing. The advantage is that it can be used at range—20 feet with a normal attack roll, 60 feet with a disadvantaged attack roll. The disadvantage, as implied by my previous sentence, is that the brick has a chance of failure proportional to how strong your ally's armor is—and this chance does not diminish just because you're in melee/Potion range. And even if the hit successfully lands, there's a non-trivial chance that the damage from the brick being an Improvised Weapon will result in the character taking more damage than what they were healed for.
So if you're in a situation where you need to desperately ensure an ally doesn't die after taking a blow that put them unconscious, this item is going to be a risk even in melee range. In terms of power level (or rarity), it shouldn't be above a Potion of Healing, and maybe arguably is behind it.