As the world continues towards autonomy, the need for continuous, precise, and robust navigation is becoming increasingly important. A new wave of modernized Global Navigation Satellite Systems (GNSS) signals are currently being implemented on the latest satellite blocks. The focus of this work is on the Global Positioning System (GPS) L5 signal, and while it is not yet fully available there are now windows of time where experimental data can be used to test modified algorithms exploiting the nature of the new signal structures. The GPS L5 signal is a Quadrature Phase-Shift keying (QPSK) signal that has both an in-phase (data) and quadrature (pilot) arm in the signal that are transmitted together. The pilot channel is not modulated with a data message which historically limits the length of coherent integration during tracking. This work adapts a vector tracking algorithm, which has been shown in prior works to provide a more robust navigation solution than scalar tracking architectures, to the GPS L5 signal structure. The traditional vector tracking architecture for both GPS L1 and L5q independently are compared to adapted methods. For the first method, the L5i and L5q discriminator measurements are combined before being added to the Kalman filter to update the Position, Velocity, and Timing (PVT) solution and Numerically Controlled Oscillators (NCOs). For the second method, L5i and L5q are tracked independently and both provide measurements to the same filter for PVT and NCO updates. This second method removes the limit on integration lengths for the L5q channel allowing for varying extended integration lengths on this channel. All methods are post processed on live sky data from only Block IIF and III satellites and evaluated. A covariance analysis is also performed comparing the methods.