We present maps of C18O and C17O J = 2 → 1 emission toward the embedded young star L1551 IRS 5. The C17O emission traces a compact region 1900 AU in radius which is centered on the star which contains 0.1 Msun of material. The integrated C17O emission has a crosslike structure aligned in the cardinal directions which is very similar to the structure seen in the submillimeter continuum emission from this source. A spatially more extended component of material which contains an additional 0.1 Msun of material within 20" of IRS 5, also contributes to the C17O emission. The cross gas is warmer and has a larger velocity dispersion than the more extended gas. The motions of the extended material imply a virial mass of 1-3 Msun, which is dominated by the mass of the central star plus disk. The C18O lines have considerable line wing emission and part of the cross is evident in this wing emission. Comparison with existing maps of the outflow near IRS 5 suggests that the cross material is part of the heated wall of the cavity evacuated by the outflow. The presence of such structures near embedded stars complicates the search for accreting material. However, the properties of the extended C17O emission constrain the mass accretion rate in L 1551 IRS 5 to be less than 1.4 × 10-5 Msun yr-1. Comparison with the observed mass outflow rate from IRS 5 at a similar size scale suggests that there is currently little or no net accretion of material from the larger scale dense core into the central 2000 AU radius region about IRS 5.