The iPhone maker's stock peaked at $342.89 during the trading day, before falling back slightly to close at $340.08, up 0.9 percent. The market capitalisation is set to reach $4.994 trillion on Wednesday.
Only AI giant Nvidia has achieved a market capitalisation of more than $5 trillion before - that happened in October last year.
However, Apple is once again the world's largest company by market capitalization, after Monday's sharp decline for Nvidia.
Nvidia closed up 0.25 percent on Tuesday and now has a market capitalisation of $4.771 trillion.
