The secret Discovery Battlestar of the fifth week of Season 8 can be found on the cliff at the base of the volcano.
To actually make the battlestar appear, you must first complete a full set of weekly challenges (weeks 1-10).
Once any four sets of them have been completed, this secret Battlestar can be collected and the challenge “Find the Secret Battlestar in Loading Screen #5” will appear in the Discovery Challenges. It will reward you with one full battle pass tier.