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For the fifth Painlev\'e transcendents an asymptotic representation by theJacobi $\mathrm{sn}$-function is presented in cheese-like strips along genericdirections near the point at infinity. Its elliptic main part depends on asingle integration constant, which is the phase shift and is parametrised bymonodromy data for the associated isomonodromy deformation. In addition, undera certain supposition, the error term is also expressed by an explicitasymptotic formula, whose leading term is written in terms of integrals of the$\mathrm{sn}$-function and the $\vartheta$-function, and contains the otherintegration constant. This paper contains corrections of the Stokes graph andof the related results in the early version.

Elliptic asymptotic representation of the fifth Painlev\'e transcendents