FIG. 1 is a front view of a first embodiment of a slim gear box, showing our new design. FIG. 2 is a rear view thereof. FIG. 3 is a right side view thereof. FIG. 4 is a left side view thereof. FIG. 5 is a top plan view thereof. FIG. 6 is a bottom plan view thereof. FIG. 7 is a bottom rear side perspective view thereof. FIG. 8 is a front view of a second embodiment of the slim gear box, showing our new design. FIG. 9 is a rear view thereof. FIG. 10 is a right side view thereof. FIG. 11 is a left side view thereof. FIG. 12 is a top plan view thereof. FIG. 13 is a bottom plan view thereof. FIG. 14 is a bottom rear side perspective view thereof. FIG. 15 is a front view of a third embodiment of the slim gear box, showing our new design. FIG. 16 is a rear view thereof. FIG. 17 is a right side view thereof. FIG. 18 is a left side view thereof. FIG. 19 is a top plan view thereof. FIG. 20 is a bottom plan view thereof. FIG. 21 is a bottom rear side perspective view thereof. FIG. 22 is a front view of a fourth embodiment of the slim gear box, showing our new design. FIG. 23 is a rear view thereof. FIG. 24 is a right side view thereof. FIG. 25 is a left side view thereof. FIG. 26 is a top plan view thereof. FIG. 27 is a bottom plan view thereof; and, FIG. 28 is a bottom rear side perspective view thereof. The broken line showing of environmental structure is for illustrative purposes only and forms no part of the claimed design.