  We report high-resolution CO(1-0) observations in the central 6 kpc of the
LINER galaxy NGC 5005 with the Owens Valley Radio Observatory millimeter array.
Molecular gas is distributed in three components - a ring at a radius of about
3 kpc, a strong central condensation, and a stream to the northwest of the
nucleus but inside the 3 kpc ring. The central condensation is a disk of about
1 kpc radius with a molecular gas mass of 2 x 10^9 M_sun. The stream between
the 3 kpc ring and the nuclear disk lies on a straight dust lane seen in the
optical. If this material moves in the plane of the galaxy, it has a velocity
offset by up to ~ 150 km/s from galactic rotation. We suggest that an optically
inconspicuous stellar bar lying within the 3 kpc ring can explain the observed
gas dynamics. This bar is expected to connect the nuclear disk and the ring
along the position angle of the northwest stream. A position-velocity cut in
this direction reveals features which match the characteristic motions of gas
in a barred potential. Our model indicates that gas in the northwest stream is
on an x_1 orbit at the bar's leading edge; it is falling into the nucleus with
a large noncircular velocity, and will eventually contribute about 2 x 10^8
M_sun to the nuclear disk. If most of this material merges with the disk on its
first passage of pericenter, the gas accretion rate during the collision will
be 50 M_sun/yr. We associate the nuclear disk with an inner 2:1 Lindblad
resonance, and the 3 kpc ring with an inner 4:1 Lindblad resonance. The high
rate of bar-driven inflow and the irregular appearance of the northwest stream
suggest that a major fueling event is in progress in NGC 5005. Such episodic
(rather than continuous) gas supply can regulate the triggering of starburst
and accretion activity in galactic nuclei. (abridged)
