Sorry, can't help with info about repeat - but do try to watch it on iplayer. It was really super. The Beeb at its absolute best. Tennant and Serkis were awesome.
But, there is some sexual content (Einstein's relationship with Else - serious heavy breathing kissing & lifting of skirts)
& intimation of homoerotic love between Eddington and Marston (though not depicted - actually doubt this wd be a problem, unless you are uneasy about homosexuality - hope not!)
so not sure how you'd feel about your 5-yr old watching that.
Also, there is a v. distressing scene where chlorine gas is tested on some pigeons which are shown dead. This would be very upsetting for a 5yr old, I should think. And it would also lead, I expect, to an explanation of how that gas was used against men. And several of the characters' sons (and Marston) are reported to have died in battle - again, v. upsetting
On the other hand, its explanations of scientific problems and its description of Einstein's vision of the universe were beautifully comprehensible, and a 5yr old might enjoy this.
And it was a celebration of science and human knowledge as transcendent of national divides, etc. which is always a lovely thing.
V. powerful & moving.