We demonstrate a self-seeded gain-switched Fabry-Perot laser diode (FP-LD) for simultaneous generation of stable picosecond pulses at five close wavelengths. The principle of the laser is based on filtering the spectrum of one of the FP-LD modes with a tunable spectrum-split fiber Bragg grating (FBG). In addition to two wavelengths produced from the reflection end of the FBG, three more wavelengths can emerge from the transmission end of the FBG when the laser is adjusted properly. The pulse characteristics can be adjusted by controlling the gain-switching frequency and the temperature of the FP-LD and the separation of the reflection peaks of the FBG. The tradeoffs in balancing pulse intensities, optimizing side-mode-suppression ratios, and equalizing wavelength separations are studied. We also demonstrate the scalability of the laser by cascading another FBG to select a different mode of the FP-LD, which defines another set of five wavelengths. To switch from one set of wavelengths to the other, we only need to adjust the gain-switching frequency and the temperature of the FP-LD. This laser is perhaps the most cost-effective one demonstrated so far for the generation of multiwavelength picosecond pulses with close wavelength separations.