Troubleshooting GFCI Outlet Tripping
Breaker --> light switch (inside) --> GFCI outlet (outside) --> 3 outlets / 2 fans


It is either the GFCI outlet itself (doubtful, because you replaced it) or one of the 3 outlets or 2 fans. "10 minutes or so" isn't the greatest for troubleshooting, but not too bad. Your choices for troubleshooting are "one at a time" or "binary". I would go for "binary" if you can. This is also "divide and conquer".


Find an (approximate) midpoint if there is a chain from GFCI to the 3 outlets and 2 fans, and disconnect the wires there and see if the problem still occurs. If it does, then you know which 1/2 has the problem (unless there is more than one problem!) and can divide further.


or


Disconnect (and cap for safety with wire nuts) wires going to 1/2 the devices and see if the problem still occurs. If it does, then you know which 1/2 has the problem (unless there is more than one problem!) and can divide further.


Which method will be easier depends on whether the devices are in more of a "chain" or a "star" configuration.