a 2x4 will support that weight without problem. But the screw connect the 指力板 with stud has its limit. Let do some math.
5kg + 70 kg = 75 kg, by engining standard you have to design for
75kg X 3 = 225 kg. if every screw can hold 15 kg dead weight. 225/15 = 15 screws
I will recommand you buy a strong piece of wood at lest 3 feet long 1 feet wide. 3/4 inch thick. bolt 指力板 to it. Then screw that board to three studs behind drywall with at least 15 screws.