Most Bible timelines puts Exodus 7-14 at one year (around 1446 BC).
The Fifth Plague of Exodus 9 destroys all of the Pharaoh's live stock including horses.
Seems that Exodus 7-14 should be over many years, even a generation to allow Pharaoh to re-establish his herd of horses for the pursuit of the Israelites in Exodus 14.
Shouldn’t Exodus 7-14 be longer than one year?
You offer one solution to the question, "If the fifth plague killed all his horses, where did Pharaoh get horses to attack the Israelites?"
Your proposal contradicts the immediacy evident in the text--there is no room for a years-long hiatus. Therefore, the plague did not actually kill ALL the horses. This is made explicit in the seventh plague, hail, when Moses warns the Egyptians to bring their livestock indoors. Thus, they were not already ALL dead.
Rather, it was hyperbole, and we are meant to understand it as such. The main intent was to describe the fact of a devastating event, not to detail its extent. Clearly, most of the horses died, but enough remained.