We present velocity-resolved Stratospheric Observatory for Infrared Astronomy (SOFIA)/upgrade German REceiver for Astronomy at Terahertz Frequencies observations of [O I] and [C II] lines toward a Class I protostar, L1551 IRS 5, and its outflows. The SOFIA observations detect [O I] emission toward only the protostar and [C II] emission toward the protostar and the redshifted outflow. The [O I] emission has a width of similar to 100 km s(-1) only in the blueshifted velocity, suggesting an origin in shocked gas. The [C ii] lines are narrow, consistent with an origin in a photodissociation region. Differential dust extinction from the envelope due to the inclination of the outflows is the most likely cause of the missing redshifted [O I] emission. Fitting the [O I] line profile with two Gaussian components, we find one component at the source velocity with a width of similar to 20 km s(-1) and another extremely broad component at -30 km s(-1) with a width of 87.5 km s(-1), the latter of which has not been seen in L1551 IRS 5. The kinematics of these two components resemble cavity shocks in molecular outflows and spot shocks in jets. Radiative transfer calculations of the [O I], high-J CO, and H2O lines in the cavity shocks indicate that [O I] dominates the oxygen budget, making up more than 70% of the total gaseous oxygen abundance and suggesting [O]/[H] of similar to 1.5 x 10(-4). Attributing the extremely broad [O I] component to atomic winds, we estimate an intrinsic mass-loss rate of (1.3 +/- 0.8) x 10(-6) M-circle dot yr(-1). The intrinsic mass-loss rates derived from low-J CO, [O i], and H i are similar, supporting the model of momentum-conserving outflows, where the atomic wind carries most momentum and drives the molecular outflows.