I don't know much about brifters, but I now have a set of Shimano 105 5500 Flight Decks.
(Interestingly, I'm gathering the group before even having a frame to put it on!)

I read about flushing with WD-40, and then using Tri-Flow, but don't know exactly how to do it.
Squirt while advancing and retracting, I assume, and spray all around the mechanicals?
Leave the hoods on? Best to let the shifters dry for several days before Tri-Flow?

Sorry if this is kind of a "Captain Obvious" post, but I want to prep these brifters the best I can, for longevity and reliability.

Thanks in advance!

I've always done it with the levers on the bike - remove the cable, put the spray hose in the cable hole and spray while shifting back and forth, then pull the brake lever forward and spray from above. The runoff drips out under the levers and doesn't touch the hoods. Once the levers are unstuck you can add triflow, I can't see any real advantage in waiting for them to dry, because any residual wd40 will simply act as a carrier.

The runoff will tend to creep under the hoods and can be a big problem in itself unless the bike is kept pointed sharply downhill during the flush out.

So do pay attention to this, and keep a bucket under the levers or the oil will hit the ground and splash all over rims, tires, shoes, etc.

Outside I put the bike against the railing and lift the rear wheel a couple of feet upward, then secure the wheel and bike to the upper run of the railing.
I actually reposition the bike to the other side before spraying out the other lever (if needed), because I want un obstructed access to the lever with the spray.

And, if the lever still works when it is warm, or if the lever is moved Veeeery slowly, then there is NO need to use the WD40.
Simply spray out the innards with a foaming oil product like shown below, which contains enough solvent to creep into the fine annular spaces about the pawl pivot pins.
Allow the lever to drip out for 20 minutes, and have a towel wedged up between the levers to soak up the settling oil. Stuff towel under the levers also to pull excess oil out from around the lever pivot spring.
It is not unheard of for the oil to make it's way into a cable housing, which can draw dirt into the housing and affect shifting quality. So be aware if any shifting hesitation is noted afterward.

this video might help

WD40 three times then the tri-flo (marginally) worked for me on RSX shifting..
I did not re-wrap the bars for days and left the bike in the summer sun (max ooze factor).

I like CRC PowerLube in the red can. About $3 at auto parts stores. Has PTFE (Teflon) for lube as well as being a solvent, so no need for WD-40 followed by Tri-Flow.

Great feedback, and brifter flushing methodology...thanks again!
The brifters are off the bike, so I should be able to prep them pretty easily.

I like the $3 Powerlube idea, sure can't beat the price.

PS: I'm hunting for a 5500 long-cage RD, and crank set, in case anyone has these kicking around a parts bin...

Since you have them off the bike I suggest carefully removing the hoods, don't want to hurt them since these are hard to get these days.
The locations of the pawls on these shifters are: 1. Near the location where the B (smaller) lever enters the body. This is behind the A(main/brake) lever above the screw that is in the A lever. 2. At the top of the mechanism between the cable installation hole and the cable exit hole. These pawls are the ones that usually causes problems.
Good luck.

Aye, if you have them off already, pull the hoods. Shimano recommends putting them in a container and filling it with enough degreaser to cover them. Allow it to work, blow them dry/rinse with high-test alcohol, and then relubricate with a light oil.

I always felt that trying to fully clean out an STI lever might be a fool's errand, given that there is typically a huge quantity of stationary dirt buildup inside and adjacent to the mechanism that does no harm as it is stationary. Once a solvent is used to break up the clumped dirt, it does tend to migrate into the moving clearances and cause a very gritty feel to the actuation. It would take extensive flushing (after dissolving of the dirt) to really clean it out to even a 90% cleanliness level imo.
Note that in this context, WD40 is not an aggressive solvent, though does penetrate just enough to thin the grease that is gumming the pawl pivots. Working the lever through just part of it's travel, not enough to make a click, is fully sufficient to actuate the pawl, and repeated tapping of the small lever thus is enough to allow WD40 or oil to free up the pawl pivot well.
But WD40 will tend to dry out and allow the pivots to become sticky after a month or three if the flushing was brief, while oil keeps on working for years when applied the same way.
Which is why I recommended that for levers that still have pawl movement (however slow or inconsistent, as when shifting a warmed lever, or moving the lever at sloth speed) be treated first with the oil-bearing lubricant, before any solvent fills the gaps first and disturbs what can be a PILE of stationary dirt.
I chose the Liquid Wrench Lubricating Oil aerosol product because of it's generous light-oil content (that offers lasting lubrication) and it's foaming action (which expands to reach all of the internal moving parts).

Alternately, and with some gummed levers that don't work even at any sloooow speed of lever movement, I have stripped off the hoods and placed the levers in an insulated small pail of hot motor oil, pre-heated (using a double-broiler approach) to 170F. I leave the levers in the hot oil for two hours before testing them, and if good then "whirling them out" on a bungee cord out in the yard, while still hot, to remove all excess oil.