When Jaime plunged into the water at the end of "The Spoils of War" on Game of Thrones, it wasn't immediately apparent that he would be surfacing again afterwards. He had just seized the opportunity to take out Daenerys, living up to his royalty-slaying reputation by charging at her on horseback with a spear in his hand. But Dany's dragons don't take kindly to people threatening their mother, and Drogon's ensuing stream of fire would have roasted Jaime alive had Bronn not jump-tackled him into the nearest lake. While it may have saved Jaime from a fiery death, these clues Jaime dies on Game of Thrones may prove that it consigned him to a watery one.
Jaime wasn't in the promo for Episode 5, but that isn't necessarily a bad omen. The show doesn't want to give up the reveal about whether Jaime is alive or dead too easily, so it makes sense that it would be mysterious about the next episode. However, some of the things Nikolaj Coster-Waldau told Entertainment Weekly about the episode might be more worrying. Apparently the episode's script direction made it quite clear: "One of our main characters is about to die." That's definitely cause for concern.
And it doesn't stop there. After calling Jaime a idiot for thinking he could dispose of Dany in one fell swoop, Coster-Waldau said that in the long term (taking his relationship with Cersei into account as well), "It's not going to end well for Jaime Lannister, I can't imagine." With statements like that coming from behind-the-scenes, it's not looking good for Jaime. He barely seemed conscious when he went under the water, plus he was weighed down by armor and a heavy golden hand. Jaime might be a goner.
However, the opposite could just as easily be true. Though it seems a main character is not long for this world, that isn't a guarantee that Jaime will be the one to die; Bronn also took a dive, and he might be the one who loses his life in the process. And despite the impressive pyrotechnics of the battle, it would be an underwhelming end to Jaime's story — one without much greater narrative significance than "people you like can die during war" — especially since Jaime's story seems far from done.
Though Jaime is very much a morally gray character, his struggle for redemption has been a compelling part of the series. It makes him a particularly interesting foil for Cersei as she descends deeper and deeper into power-hungry madness. Without Jaime, who would act as an even slightly mollifying influence on her? No one. It would just be Cersei and Euron burning it all down.
Jaime may not meet a happy ending when Game of Thrones finishes for good, but despite evidence to the contrary, it just doesn't seem like his time yet.