Wow — the idea of a 'book 5' picking up after 'Inheritance' fires up so many little mental fireworks for me. The most obvious bridge is that 'Inheritance' ends with massive change: the old tyrant falls, power structures wobble, and a handful of characters are effectively sent off in new directions. So any continuation would almost certainly start by dealing with the fallout — political, emotional, and magical. I’d expect the first section to feel like a slow, sometimes painful unpacking: councils and treaties, grieving for losses, and the awkward practicalities of rebuilding cities and alliances.
From there, I’d want book 5 to take the character threads that were left semi-open in 'Inheritance' and deepen them rather than just filling in plot boxes. Think of it as switching from battle-setpiece momentum to quieter, character-focused arcs: the responsibilities of new leadership, the moral cost of decisions made in war, and those personal journeys like the ones Eragon and Arya begin at the end. There are also smaller mysteries and worldbuilding hooks sprinkled through the series — scattered lore about dragon history, the role of the Eldunarí, and the consequences of magic use — and a fifth book could use them to expand the setting without retreading old ground.
If you like the tone of 'Brisingr' or the introspection of 'Eldest', expect book 5 to mix political chess with more intimate scenes. And if the author dips into short-story collections like 'The Fork, the Witch, and the Worm' for side detail, that could enrich the main narrative nicely. Personally, I’d be thrilled if it balanced the grandeur of the final battle with quieter chapters that let the world breathe — those are the moments that stick with me most.