  Properties of hypernuclei $_{\Lambda \Lambda}^5$H and $_{\Lambda \Lambda
}^5$He are studied in a two-channel approach with explicit treatment of
coupling of channels ^3\text{Z}+\Lambda+\Lambda and \alpha+\Xi. Diagonal
\Lambda\Lambda and coupling \Lambda\Lambda-\Xi N interactions are derived
within G-matrix procedure from Nijmegen meson-exchange models. Bond energy
\Delta B_{\Lambda\Lambda} in $_{\Lambda \Lambda}^5$He exceeds significantly
that in $_{\Lambda \Lambda}^5$H due to the channel coupling. Diagonal \Xi\alpha
attraction amplifies the effect, which is sensitive also to \Lambda-core
interaction. The difference of the \Delta B_{\Lambda\Lambda} values can be an
unambiguous signature of the \Lambda\Lambda-\Xi N coupling in \Lambda\Lambda
hypernuclei. However, improved knowledge of the hyperon-nucleus potentials is
needed for quantitative extraction of the coupling strength from future data on
the \Lambda\Lambda hypernuclear binding energies.
