The fifth house in Lilly's catalogue is a fair picture of what the seventeenth century took recreation to be: children, pleasure, banquets, ale houses, taverns, plays, and messengers and ambassadors. It is the house of enjoyment taken publicly and in company.
The organising idea is the one that also puts children there. The fifth is what a life produces for its own delight, as against the second house, which is what a life accumulates. A play, a feast and a child are all issue, and the tradition groups them by that rather than by any modern sense of category.
The Sun has a claim on the house because Leo is the fifth sign and the Sun rules Leo, and because the Sun's own signification, display, generosity and the visible centre of a gathering, matches the material well. Venus has the stronger claim in practice: the fifth is where Venus has her joy, one of the seven houses in which a planet is held to be at home in its own affairs whatever sign occupies it. A benefic in her joy in the house of pleasure is about as unambiguous as traditional astrology gets.
Jupiter contributes abundance rather than pleasure as such. The distinction the tradition draws between the two benefics is worth keeping. Venus supplies the sweetness of a thing and Jupiter its plenty, and a reading that treats them as interchangeable has lost the difference between a good evening and a large one.