The Battlerager's Reckless Abandon feature says:
Beginning at 6th level, when you use Reckless Attack while raging, you also gain temporary hit points
The Reckless Attack feature says:
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.
Since Reckless Attack only triggers when you make your first attack on your turn, it can only be used once per turn (and only on your turn, unlike Sneak Attack). Therefore, you can only gain the benefit of Reckless Abandon once per turn.
Also, as Purple Monkey points out, temporary HP from multiple sources does not stack, so even if you could use Reckless Abandon multiple times on your turn, you'd still only have 5 Temp HP: How does Armor of Agathys interact with getting temporary hit points?