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The expression can be simplified by combining like terms:
\begin{align*}
\left(3xy + 2xz + yz\right) + \left(2xy - 4xz + 5yz\right) &= 3xy + 2xy + 2xz - 4xz + yz + 5yz \\
&= (3xy + 2xy) + (2xz - 4xz) + (yz + 5yz) \\
&= 5xy - 2xz + 6yz
\end{align*}
Therefore, the expression is equivalent to \boxed{5xy - 2xz + 6yz}.