  We construct the full effective action including DBI and WZ terms for
solitonic 5-branes covariant under T-duality. The result is a completion of
results known in the literature to a full T-duality covariant expression. The
covariant WZ action includes previously omitted R-R terms. The obtained full
covariant effective action reproduces the one obtained by S-duality from the
D5-brane upon the correct choice of the covariant charge.
