Are there distinct primes $p,q$ satisfying $pq=(2^r-1)(p+q)-5$? We let $p\neq q$ be odd prime numbers and $r$ be integer $>2$.
Are there such $p,q$ satisfying $pq=(2^r-1)(p+q)-5$?
This is clear from here that, 
$q(p-2^r+1)=(2^r-1)p-5$, 
and $p(q-2^r+1)=(2^r-1)q-5$.
Thanks.

Over at tomerg's other, closely-related question The form $xy+5=a(x+y)$ and its solutions with $x,y$ prime I found $p=17179929661$, $q=4880269588100161$, $r=34$ is a solution. 
