  We construct two new SL(2,Z) invariant vacua of type IIB string theory which
are bound states of $(p,q)$ strings with $(m,n)$ 5-branes, written as ((F, D1),
(NS5, D5)) and preserve 1/4 of the full space-time supersymmetries. For the
first case, the strings live inside the 5-brane world-volume and in the second
case the strings are perpendicular to the 5-brane world-volume. In the first
case, naively one would expect an attractive interaction between the strings
and the 5-branes due to attractive force between F and D5 and also between D1
and NS5. We find that 1/4 BPS bound state exists only when the vacuum moduli
satisfy certain condition which is found to be consistent with the no-force
condition between the branes. No such complication arises for the second case.
The tension formulae and the various other descendant states which can be
obtained by the application of T-duality for both these bound states are
discussed.
