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 bars 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)
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