By the way
Are the numbers with k=5359 and an exponent smaller than the new prime going to be tested?The server won't actively try to kill pending tests for k=5359. No new ones have been assigned in over a week so there aren't that many. If you have one, feel free to drop it. The server is already configured to not reassign it.
I think it makes sense in order to prove that the new prime is the smallest one with k=5359. That could be useful for statistical purposes.