When I have been to Rio in May the weather has always been warm to hot with a few days of rain now and then. I think that May is what would be considered Fall for those of us above the Equator but Fall in Rio is often like summer in Houston I have found.
As to your arrival and the availabilty of Taxis and such: if you actually arrive at 5am, by the time you de-plane, go through immigration, get your luggage and then pass through customs it will be closer to 6am. I believe (but do not know for certain) that the taxi stands and the money exchange stand will be open for business by that time.
My first stop after getting past customs is the money exchange booth just outside the doors as you exit the baggage area (this only applies if you are landing at Tom Jobim Intl. Airport in Rio de Janeiro). There I exchange US dollars for Brasilian currency. I have found the rates of exchange at these booths to be much better than those offered by hotels and sometimes equal to or slightly better than Banco du Brasil. After I have converted my currency at the airport exchange office, the radio-dispatched taxi stands are just a couple of steps away. At these taxi stands you can pre-pay for a round-trip to your hotel and then back to the airport on the day you check out. The round-trip costs between $40 and $60 dollars US (less in Euros) dependent upon fluctuations in the exchange rates.
I like these pre-paid or "flat-rate" taxis as I don't have to worry about a driver trying to jack-up the fare by taking the "long" way to my destination and they are air-conditioned and as safe as one can hope for in Rio.
Finally, I do carry Travelers Cheques but only to pay my hotel bill. Most stores do not accept Travelers Cheques (though you would have no problem using them at places like H. Stern or other "high-end" stores) and trying to convert Travelers Cheques into ready cash can be a hassle even when dealing with a big bank. Like I stated, I only really use them to pay my hotel bill because I have found that when the hotel places a hold on your credit card, to cover the stay, they usually hold alot more than is necessary thereby blocking your access to funds you think are not encumbered. Far easier for me to pay the hotel with Travelers Cheques and use my credit card for incidentals as they arise.
This is what works for me. I am sure that you will get many responses to your posting and each will have its own merit and traveler wisdom for you to mull over before your trip.
Safe travels to you!