Correlations of Almost Primes

Let $p_1,\ldots,p_5$ be primes with $p_1p_2,p_5\in(X,2X]$, let $h$ be a non-zero integer and $A > 3$. Supposing that $p_1,p_3$ lie in a certain range depending on $X$, we prove an asymptotic for the weighted number of solutions to $p_3p_4=p_1p_2+h$ which holds for almost all $0 5$.