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In 2010, quantum anomalous Hall effect (QAHE) in graphene was proposed in the presence of Rashba spin-orbit coupling and ferromagnetic exchange field. After a decade's experimental exploration, the anomalous Hall conductance can only reach about 0.25 in the units of $2e^2/h$, which was attributed to the tiny Rashba spin-orbit coupling. Here, we theoretically show that Re-intercalation in graphene/CrI$_3$ heterostructure can not only induce sizeable Rashba spin-orbit coupling ($>$ 40~meV), but also open up large band gaps at valleys $K$ (22.2 meV) and $K' $ (30.3 meV), and a global band gap over 5.5 meV (19.5 meV with random Re distribution) hosting QAHE. A low-energy continuum model is constructed to explain the underlying physical mechanism. We find that Rashba spin-orbit coupling is robust against external stress whereas a tensile strain can increase the global bulk gap. Furthermore, we also show that Re-intercalated graphene with hexagonal boron-nitride can also realize QAHE with bulk gap over 40~meV, indicating the tunability of $5d$-intercalated graphene-based heterostructure. Our finding makes a great leap towards the experimental realization of graphene-based QAHE, and will definitely accelerate the practical application of graphene-based low-power electronics.