Problem with calculating the correct value for $(p-1)*(q-1)$?
So, you're given the exponents (and the ciphertext), and are expected to recover the modulus?  That's certainly not the standard way of using RSA.

It turns out that the necessary and sufficient conditions on $p, q$ is that $p-1, q-1$ are factors of $ed-1$; hence we know that $p, q \in \{ 3, 5, 11, 17, 41 \}$ (as those are the primes that meet this criteria), and any such combination of distinct $p, q$ would work (we also know that $pq &gt; c$, however all combinations meet this criteria); by work, I mean that $(m^e)^d \equiv m \bmod{pq}$ for all messages $m$.  Now, with some combinations, the $e, d$ combination might not be minimal; however nonminimal $e, d$ values do happen in practice.

As both $p, q = 5, 11$ and $p, q = 3, 11$ meet the above criteria, both lead to valid answers.  If the original question did not add any additional information, well, they did not specify the question sufficiently.