FIG. 1 is an isometric view of the wipes dispensing system, embodying the new design;

FIG. 2 is a front view thereof;

FIG. 3 is a back thereof;

FIG. 4 is a left view thereof;

FIG. 5 is a right view thereof;

FIG. 6 is a top view thereof;

FIG. 7 is a bottom view thereof;

FIG. 8 is an isometric view of a second embodiment of the wipes dispensing system, embodying the new design;

FIG. 9 is a front view thereof;

FIG. 10 is a back thereof;

FIG. 11 is a left view thereof;

FIG. 12 is a right view thereof;

FIG. 13 is a top view thereof;

FIG. 14 is a bottom view thereof;

FIG. 15 is an isometric view of a third embodiment of the wipes dispensing system, embodying the new design;

FIG. 16 is a front view thereof;

FIG. 17 is a back thereof;

FIG. 18 is a left view thereof;

FIG. 19 is a right view thereof;

FIG. 20 is a top view thereof;

FIG. 21 is a bottom view thereof;

FIG. 22 is an isometric view of a fourth embodiment of the wipes dispensing system, embodying the new design;

FIG. 23 is a front view thereof;

FIG. 24 is a back thereof;

FIG. 25 is a left view thereof;

FIG. 26 is a right view thereof;

FIG. 27 is a top view thereof;

FIG. 28 is a bottom view thereof;

FIG. 29 is an isometric view of a fifth embodiment of the wipes dispensing system, embodying the new design;

FIG. 30 is a front view thereof;

FIG. 31 is a back thereof;

FIG. 32 is a left view thereof;

FIG. 33 is a right view thereof;

FIG. 34 is a top view thereof; and,

FIG. 35 is a bottom view thereof.

The broken lines shown in the drawings are for illustrative purposes only and form no part of the claimed design.