We extend our previous construction of global solutions to Type IIB
supergravity that are invariant under the superalgebra $F(4)$ and are realized
on a spacetime of the form $AdS_6 \times S^2$ warped over a Riemann surface
$\Sigma$ by allowing the supergravity fields to have non-trivial $SL(2,{\mathbb
R})$ monodromy at isolated punctures on $\Sigma$. We obtain explicit solutions
for the case where $\Sigma$ is a disc, and the monodromy generators are
parabolic elements of $SL(2,{\mathbb R})$ physically corresponding to the
monodromy allowed in Type IIB string theory. On the boundary of $\Sigma$ the
solutions exhibit singularities at isolated points which correspond to
semi-infinite five-branes, as is familiar from the global solutions without
monodromy. In the interior of $\Sigma$, the solutions are everywhere regular,
except at the punctures where $SL(2,{\mathbb R})$ monodromy resides and which
physically correspond to the locations of $[p,q]$ seven-branes. The solutions
have a compelling physical interpretation corresponding to fully localized
five-brane intersections with additional seven-branes, and provide candidate
holographic duals to the five-dimensional superconformal field theories
realized on such intersections.