There might be a bit too much focus on Forgotten Realms or Eberrons here, and not enough what would make a 5E setting different and how to present the core races of the game in that setting differently from FR (or Eberron).
One way would definitely be to actually establish home countries or major settlements and organizations where each core species is relevant. They should probably be also situated in the "main adventuring" area of the setting, not just on the fringes (which doesn't mean that there might not be at the fringes, too. But there should be a few spaces more centrally, as well.)
For example:
Central Area of Interest might be a large valley situated between the Easter and Northern Mountains and the South Sea and the Western Forests. A large Empire existed once in this area, but it broke apart in the great succession wars, leaving behind several smaller kingdoms and fiefdoms, many still controlled by the remnants of the houses originally fighting each other. Most of the houses were humans, from the original smaller kingdoms that eventually were united into the Emipre, but as the Empire started trading with the neigboring cities and nations, people of these nations joined, and some founded their own house.
The Goliaths main country is from the Eastern Mountains, but along the rivers to the south sea, they have many settlements, some of them mixed strongly with humans and halflings, the humans having formed communties to the fruitful central lands and the halflings having used the rivers for trade and transportation for centuries. They originally came from the South Sea from another continent, and the place of their original landing still holds one of the largest Goliath settlements - even though it formally isn't part of the Goliath nation.
The Dwarves hail from the Northern Mountains. They were once enslaved by the Giants, but as a new Empire was forming in the Central Valley, it offered them help in exchange for supporting the empire's defense. This lead to the erection of Dwarven fortresses inside the valley, and several dwarven dominated settlements also exist along the rivers from the Northern Mountains to the South Sea.
The Dwarves share the Souther Mountains with a Dragonborn nation which is siutuated in area that is dominated by volcanic area. The Dragonborn nation is only a shadow of its former self after one of the volcanos erupted and destroyed its capitcal city, many Dragonborns living in diaspora now. The largest dragonborn city is now one of the Dwarfen Fortresses, given to allow the displaced Dragonborn a place, in exchange for military service and gold from the dragonborn nation's hoard. Not everyone is favorable with this deal, some Dwarves think the fortresses need to go back in Dwarven hands, and some Dragonborn think the price they paid was too high.
The Elves hail from the Western Forests. They didn't have much interest in the central valley, but when the Succession War started, they feared it spilling over, and a lot of people tried to flee the war into the forest. The Elves expanded into the valley when they saw the succcession war consume the country, and to fight the influx of the people fleeing the wars into their forests. They built cities at the edges of the remaining central valleys forests as safe haven for those fleeing from the war. When the Elves build cities, they discovered and inadvertantly activated several fey crossings, leading to an influx of Goblins and Gnomes. The latter easily adapted to the place, and formed settlements in the valley, or joined existing ones. Building those cities however wasn't welcomed by the houses, and it forced the Elves to fight against some of them, which ultimately lead to the current unstable peace. Some are still angry at the Elves, because they are sure their house would have won the succession war, but many also think of them as peacekeepers, a position the Elves do not always feel comfortable with, but has also provided them many opportunities.
It is unclear whether the Orc or the Humans or both are native to the central valley, but they coexisted for a long time until the human started to focus on agriculture and city-building. This lead to many violent conflicts, and the Orc adopting a more martial attitude, as the wilderness they once roamed had turned into cultivated land, forcing them to raid. One Orc chieftain decided to change all this, and united the Orc tribes in a war - intiailly conquering and destroying several settlements before offering threatened settlements a new deal - allowing the Orc to trade freely and join the settlements, and demanding some lands back. Cities that disagreed were razed, cities that agreed now had
The Houses from the former Empire are still important blocks - they were aristrocats based either on former Kingdoms or from influential traders and guilds. One of the houses is composed mostly of Tieflings, as the Kingdom they were part pacted with devils to gain more power and influence, but the kingdom fell when the Devils were demanding a price even the corrupted leadership was not willing to pay. Not just the noble family, but also its citizens, were turned to Tieflings as punishment, and most of the wealth and power was lost. Generations after, the original Capital City had recovered considerably, not as powerful and influential as before, but large enough to be an important member in the founding of the Empire.
A small Aasimar settlement in the Eastern Mountains exists, predating even the Goliaths. It is said that in ancient times, a holy battle was fought their, against a primordial evil. It is said the Holy Forces were victorious, but a God was slain, leaving behind the White Scar. The place is unusual in that it's relatively temperate, but the only form of precipation is snow, so it never quite melts. It is said if the snow melts, large evil will befall the world - the last time this happened when the Last Empress fell. The place is popular for pilgrimage among all faiths.
Ooops, that was a bit more than I intended, and nothing I am really likely to follow up for myself... Anyway, don't want to throw it away either.
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