We present a study on the detailed chemical abundances of five new relatively bright $r$-process-enhanced stars that were initially observed as part of the SDSS/MARVELS pre-survey. These stars were selected, on the basis of their metallicities and carbon abundances, among a total of 60 stars, for high-resolution spectroscopic follow-up as part of the HESP-GOMPA survey (Hanle Echelle SPectrograph -- Galactic survey Of Metal Poor stArs). Here we discuss the three new $r$-I and two new $r$-II stars found in this survey. We have carried out a detailed abundance analysis for each of these stars, at a resolving power of $R sim 30,000$, and compare our results to the existing literature. We could measure three of the first $r$-process-peak elements (Sr, Y and Zr) in all five stars, while Ba, Ce, Nd, Sm, Eu, and Dy could be detected among the second $r$-process-peak elements. Thorium could also be detected in one of the targets, which is found to be an actinide-boost star. We have carried out a comparative study among the sub-populations of the $r$-process-enhanced stars and other stars of the Milky Way halo population to constrain the origin of this class of objects. These bright $r$-process-enhanced stars provide an excellent opportunity to study the nucleosynthesis history of this population in great detail, and shed light on their chemical-enrichment histories.
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