Agelmar Jagad of Shienar and Pedron Niall, Lord Captain Commander of the Children of the Light, were two of nine commanders who alternately took command of the Grand Alliance forces during the Aiel War. In fact, they were first and second respectively in the rotation. This shows that by the Aiel War they were already considered to be excellent commanders. (Other commanders were Aranvor Naldwinn, Captain-Genral of the Queen's Guard of Andor [KIA], King Mattin Stepaneos of Illian, the High Lord Astoril of Tear, Lord Aleshin Talvaen of Ghealdan, Lord Aeman Senhold of AMadicia, King Laman Damodred of Cairhien [KIA]. Not all of these were selected because of their skills as a commander; politics played a role too.)

Agelmar Jagad got his reputation in the Borderlands. As High Seat of the House Jagad he was lord of Fal Dara, the Shienaran fortification closest to the blight. This provided him with plenty of opportunity to gain his reputation.

Pedron Niall gained his reputation during the Whitecloak War (called the Troubles by the Whitecloaks). Then a Captain Commander, Perdon Niall led the Whitecloak forces in Altara. He won almost every battle, and in the one he lost he saved many of his men thanks to his tactical insight (and a 'hunch' - but that is what being a Great Captain is all about).

Rodel Ituralde is also known to have fought in the Aiel War, but not as an army commander. It is likely he gained his reputation as a Great Captain commanding sub-units, making unconventional moves much like the ones chronicled later during the war against the Seanchan forces in Arad Doman.

Davram Bashere's titles, Guardian of the Blightborder and Defender of the Heartland, should make clear how he gained his reputation as a Great Captain. Like Agelmar Jagad, his position near the Blight has given him plenty of opportunities to prove his worth.

Gareth Bryne worked his way up in the Queen's Guard of Andor. Thanks to his excellent skills he rose to become Captain Commander under Queen Mordrellen Mantear. He served Queen Morgase Trakand during and after the Third Succession War.

This is how each of them gained their reputation individually, but you also asked how these came to be accepted universally, to the point of them collectively being called the "Five Great Captains". This is more difficult to answer. It is clear that all of them have an exceptional ability to command. It is hard to say though what makes them exceptional or what they do or have what other's don't. It is not even clear that they all have the same thing that makes them exceptional. With that in mind, it is evident that these five commanders stand head and shoulders above almost anyone else in living history, and if there are five people so exceptionally different from others, it is convenient to lump them together so you have one way of referring to them all: the Five Great Captains.

This is perhaps an unsatisfactory answer, but unfortunately in history it is not always possible to give a clear and precise reason why something is the way it is.

I don't know the answer to your question, but could you please not be so derogatory in your questions? Using the designation of "Randland" instead of the Westlands really devalues the Seanchan's efforts to help unify the continent near Shayoul Ghul as well as devalues that Towers involvement in keeping the Westlands afloat during the many crisis over the millenia.