I am successful to get the last key $k_5$. Just to say some words about the implementation:
I search for a good differential, calculate the probability and generate a list of input pairs which satisfy my input difference.
I let the pairs flow through the cipher (with the unknown keys) and then I guess the key bits of the sbox in the last round who are involved in my expected differential.
Now I decrypt with my guessed key, undo the sbox and generate the difference of the pair. If it satisfys my expected value, I count it as a hit. The key with the highest counter is probably the right one. So far so good. I can recover $k_5$.
However I can not get it work with the $k_4$.
I do the following: Search for a good differential, calculate the probability and generate the list with pairs which satisfy my input difference. I let them flow through the cipher and decrypt the last round with my recovered $k_5$. Then I undo the sbox and apply my guessed $k_4$ undo the permutation and undo the next sbox. Then I generate the difference and compare to the expected...
But this does not work. Is there a general mistake in my doing here?