Given the temp spread where you live, 40F-120F, which is not too different from where I live in Florida during summer months, I would use 0-30w or 5-30w.
The 5-40w that was used on your FJ IMO is too heavy, (thick when hot) when the engine reaches operating temp. Society of Automotive Engineers (S.A.E.) who
certify all the rules ref oil performance, state that the first # (5) is the viscosity (ability of the oil to flow at a given temp) of the oil at cold start up. A "cold" start is any start that is not at full operating temp.
The 5 designates that the oil will flow at -30F and the 30W will have a specific viscosity at full operating temp which is designed by the engine manufacturer.
Bottom line, you will be fully protected using the 5W-30. This assumes you are using your FJ for "normal" type stuff. I personally use 0w-30 Mobile 1 synthetic since my FJ was new
in 2011 and with 90k on the clock it runs beautifully and I do not burn or leak 1 drop of oil. Just make sure you change your oil, IMO, at 6000 miles if you use synthetic with a new filter.
Some people on this forum go longer, but 6000 between changes is very safe. The TBN additive levels at 6k is still very adequate.
BTW, IMO the 0-20w that is in your manual was put there primarily to give the best gas mileage for these engines NOT necessarily the BEST protection. Will it damage your engine, NO.
But it is not the BEST weight for ALL applications. My FJ sees a fair amount of cold weather in Colorado too, hence the 0w-30.
The subject of oil can take weeks to fully discuss. If your interested theres tons of oil info online and in this forum. Lots of opinions too. This is just my .02......