5. Let $x$ be the length of the smaller segment. On the upper side of the quadrilateral, which has a length of 1, there are 3 small segments and one large segment. Therefore, the length of the large segment is $(1-3x)$. On the lower side of the quadrilateral, which has a length of 2, there are 3 large segments and one small segment.

We get the equation $3 \cdot (1-3x) + x = 2$.

Thus, $3 - 9x + x = 2$.

Therefore, $x = \frac{1}{8}$.

So, the length of the smaller segment is $\frac{1}{8}$. Therefore, the length of the larger segment is $1 - 3 \cdot \frac{1}{8} = 1 - \frac{3}{8} = \frac{5}{8}$.

Hence, the larger segment is five times longer than the smaller one.
Answer: the ratio $5: 1$.