Probably not, unless your 5 year-old is somehow of breeding age (the matchmaker has started to visit it) and your 20 year-old has not yet become a ojiitchi/otokitchi (grandfather/grandmother). I tried to mate an adult tama (it was about age 5 the first time) with a friend's ojiitchi and failed. Even when the matchmaker started coming for mine, my tama still wouldn't mate with the grandfather. However, my friend and I connected our tamas just after mine became a grandmother,and the 2 mated immediately (and the 4 smiley faces on the friend stats finally became hearts.) Breeding age and lifespan might depend on the generation of the tamas involved though, so perhaps there would be a way at some point to mate a 5 year-old with a 20 year-old.
Since old people can mate, and I've read that tamas can live to over 70 "years" of age, you might be able to at least mate a 10 or 11 year-old with a 75 year-old.