+5 culture is also a little over the top, imo. Sure there are plenty of other wonders with more than that, but there is more than just the direct effects to consider.
This will potentially allow a late-game city to have the following buildings active, when they otherwise wouldn't (not factoring in UBs that replace them):
Monument : +1 Culture
Walls : Not a big deal unless less advanced civs.
Castle : +1 Culture, +25% Epsionage, +1 Trade Route
Up to 7 monestaries (probably fewer) : +2 Culture, +10% science each
Stables : not that you will be making any more Mounted units.
That comes up to 2-16 culture, +1 Trade Route, +0-70% science, some very minor military advantages
Then there are all the Wonders it could reactivate..
Temple of Artemis
University of Sankore
Just reactivating 2 or 3 of those could be potentially game changing.
For the stated ability, I would go at most 2 culture and maybe 1 happy. Even at that, it would be potentially gamebreaking.
That being said, I do think it is a nifty idea.