The search for high-entropy alloys (HEAs), a new class of materials, with high magnetocaloric performance can address the open question about their potential in functional applications. HEAs exist in a vast compositional space but magnetocaloric HEAs typically exhibit modest magnetocaloric response as they undergo second-order magnetic phase transitions. In this work, through a property-directed search approach, FeMnNiGeSi HEAs with varying Ge/Si ratio are found in the large HEA space to exhibit magneto-structural first-order phase transition. Isothermal entropy change as large as 13 J kg-1K-1 (for 2.5T) is achieved, which is the largest reported to date for magnetocaloric HEAs. When compared to conventional high-performance magnetocaloric materials, our work is observed to be comparable to many of the conventional systems, closing the gap between magnetocaloric HEAs versus conventional magnetocaloric materials for the first time. This opens a new path for the search of functional materials with the optimal mechanical properties of HEAs.