The monkey shown in the picture is a gibbon. It exists in treetops and never needs to touch ground and so has come to be associated with the wisdom of long life to which Daoists aspire, and the attainment of other-worldly knowledge towards which Buddhists work.
Peach trees blossom in the early spring amid the snow, and so peaches are associated with endurance and long life. Eating a peach from the mythical garden of the Queen Mother of the West was said to assure a life span of a thousand years.