I cannot find any official details on the Far Realm for 5th edition Dungeons & Dragons. Is there any published lore on the topic or is it supposed to be open ended?
According to Dungeon Master's Guide p.68, conveniently available on the Wizards of the Coast's website as a PDF:
The Far Realm is outside the known multiverse. In fact, it might be an entirely separate universe with its own physical and magical laws. Where stray energies from the Far Realm leak onto another plane, matter is warped into alien shapes that defy understandable geometry and biology. Aberrations such as mind flayers and beholders are either from this plane or shaped by its strange influence.
The entities that abide in the Far Realm itself are too alien for a normal mind to accept without strain. Titanic creatures swim through nothingness there, and unspeakable things whisper awful truths to those who dare listen. For mortals, knowledge of the Far Realm is a struggle of the mind to overcome the boundaries of matter, space, and sanity. Some warlocks embrace this struggle by forming pacts with entities there. Anyone who has seen the Far Realm mutters about eyes, tentacles, and horror.
The Far Realm has no well-known portals, or at least none that are still viable. Ancient elves once opened a vast portal to the Far Realm within a mountain called Firestorm Peak, but their civilization imploded in bloody terror and the portal’s location—even its home world—is long forgotten. Lost portals might still exist, marked by an alien magic that mutates the area around them.
Player's Handbook, p.302, summarizes the same information.
Seeing a creature from the Far Realm can risk an individual's sanity (DMG p. 265).
Githzerai philosophers are aware of the existence of the Far Plane, and it may be connected to the aboleths somehow (MM p. 14).
Some users of wild magic are so afflicted due to contact with the Far Realm. (PHB p. 103).
Some warlocks use the ancient knowledge of beings of the Far Realm. Warlocks of the Great Old One may worship such unfathomable beings. (PHB p. 105).
Powerful, world-shattering beings known as the Elder Evils are speculated to be creatures of the Far Realm (Mordenkainen's Tome of Foes).
Far Realm lore from earlier editions of the game can also be used in your campaign. However, much about this plane is intentionally left undefined in order to set a mysterious and unsettling atmosphere, so lacking much rigidly defined lore may be to your advantage. You may find it useful to read the works of H.P. Lovecraft for inspiration.
Other than the few paragraphs in the DMG (p.68), there really isn't much, no. It's intentionally vague, both because it's a playground for a DM, and because it's meant to be essentially unknowable, a place beyond human comprehension.
There's slightly more in previous editions, and some people have done DM's Guild updates of old adventures that center around the Far Realm (notably "The Gates of Firestorm Peak", which the DMG alludes to), but even then the basic nature of the far realm is "that which man was not meant to know", so it has tended to stay pretty well unexplored throughout D&D's existence.