5. Point $P$ is located on side $AB$ of square $ABCD$ such that $AP: PB=2: 3$. Point $Q$ lies on side $BC$ of the square and divides it in the ratio $BQ: QC=3$. Lines $DP$ and $AQ$ intersect at point $E$. Find the ratio of the lengths $AE: EQ$.
Answer: $A E: E Q=4: 9$.

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