We report a mode-locked Ti:sapphire femtosecond laser with $5\mathrm{GHz}$ repetition rate. Spectral broadening of the $24\mathrm{fs}$ pulses in a microstructured fiber yields an octave-spanning spectrum and permits self-referencing and active stabilization of the emitted femtosecond laser frequency comb (FLFC). The individual modes of the $5\mathrm{GHz}$ FLFC are resolved with a high-resolution spectrometer based on a virtually imaged phased array spectral disperser. Isolation of single comb elements at a microwatt average power level is demonstrated. The combination of the high-power, frequency-stabilized $5\mathrm{GHz}$ laser and the straightforward resolution of its many modes will benefit applications in direct frequency comb spectroscopy. Additionally, such a stabilized FLFC should serve as a useful tool for direct mode-by-mode Fourier synthesis of optical waveforms.