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We consider the off-shell formulation of the 5D, $ {\cal N}$=1 superYang-Mills and super Chern-Simons theories in harmonic superspace. Using such aformulation we develop a manifestly supersymmetric and gauge invariant approachto constructing the one-loop effective action both in super Yang-Mills andsuper Chern-Simons models. On the base of this approach we compute the leadinglow-energy quantum contribution to the effective action on the Abelian vectormultiplet background. This contribution corresponds to $F^4$ invariant which isgiven in 5D superfield form.

Effective actions in ${\cal N}$=1, D5 supersymmetric gauge theories: harmonic superspace approach