Prague and Krakow are close enough that a direct train makes far more sense than flying, and both cities reward slow walking over a packed sightseeing schedule.
Days 1–3: Prague
Prague Castle, the Charles Bridge at sunrise before the crowds, and an evening in Vinohrady away from the Old Town markup. A hostel bed near Žižkov runs $14–18 a night and puts you a short tram ride from everything.
The border crossing
The direct EuroCity train from Prague to Krakow takes about 7.5 hours and costs $30–45 booked in advance through the operator's own site rather than a third-party booking aggregator that adds a markup. It's a full but comfortable travel day — pack food, since the dining car options are limited and pricier.
Days 4–5: Krakow
Two days is enough for the Old Town, Wawel Castle, and Kazimierz. Save the Auschwitz day trip for a longer future visit rather than cramming it into this short loop — it deserves a full, unhurried day.
Takeaway: Book the EuroCity train directly through the national rail operator's website, not a booking aggregator — the markup on this specific route is often 15–20%.