Cairo & Alexandria in 5 Days
Days 1, 2 & 3 -- See days 1, 2, and 3 in "Cairo in 3 Days."
Day 4: Intro to Alex -- Catch one of the morning trains to Alexandria from Ramses Station. On summer weekend (Thurs and Fri) mornings, it's essential to have bought the tickets at least 1 day in advance. Upon arrival in Alexandria, buy your return tickets to Cairo if you haven't already got them; then walk from the station to Kom el Dikka and check out the Villa of the Birds. If you got a really early start, you'll have plenty of time to walk down through Attarine past the junk stores, pausing for a cup of coffee at one of Alexandria's old coffee shops before lunch at Trianon in Saad Zagloul Square. After lunch, head over to Pompey's Pillar and the catacombs at Kom al Shaqqafa.
Dinner is going to be fish (what else?) at the Fish Market or Abou Ashraf, depending on your idea of what makes a good view. After dinner, a brief roam from Saad Zagloul Square to Cap d'Or for a beer can be fun. If you've only got the 1 night in the city, I recommend using one of the hotels close to Saad Zagloul. The Salamlik and the Helnan Palestine are possibilities, but you won't enjoy the racetrack commute up and down the 8-lane, seaside thoroughfare that they necessitate.
Day 5: Alexandria Museums -- I never go anywhere in the morning in Alexandria without a couple of coffees and a pastry from one of the cafes in Saad Zagloul Square. Spend the morning browsing through the excellent Graeco-Roman Museum and, if you have the time, the Cavafy Museum, before heading out to the Greek Maritime Club for lunch. After lunch, it's just a 2-minute walk up to the Qaitbey Fort.
Your schedule will now depend on what time you are heading back to Cairo. If you have a couple more hours, consider a loop that takes you to the Bibliotheca Alexandrina for a look at the mosaics in the basement, then to the Royal Jewelry Museum -- assuming that it has finally reopened -- before heading back to the train station. When considering this, keep in mind that until about 6 or even 7pm, the streets between the museum and the station will be jammed, and the final taxi ride could take upward of 30 minutes.
Luxor and Aswan: 5 Days of Ancient Egypt
Days 1, 2 & 3 -- See days 1, 2, and 3 in "Luxor: 3 Days of Ancient Egypt." Optional Day 4: If you're particularly keen on seeing Abu Simbel, take the early morning flight there instead of doing Philae. You can then head to Philae after dinner for the sound-and-light show.
Day 4: Aswan -- Aswan may be relatively close to Luxor, but it is very different. Take a moment to shift gears and appreciate that the pace of life is a lot slower here. Head south to the Philae temple complex first thing before the day starts to heat up. If you're going to check out the High Dam, do so on the way back from the temples, but a better way to spend your hour before lunch would be to stop by the Unfinished Obelisk. Lunch in the air-conditioned comfort of the Mövenpick, and spend the heat of the afternoon at the Nubian Museum. After that, head down to the old Aswan Museum at the southern end of Elephantine Island. The gardens around the museum are a great place to see out the day. Around sunset, catch a faluca, disembarking on the Corniche close to the Blue Moon for a simple fish dinner. Spend the evening doing a little shopping in the souk.
Day 5: West Bank -- Start the day with an after-breakfast boat ride to the West Bank and a hike up to the Tombs of the Nobles. If you've got the gas, hike over to the abandoned Monastery of St. Simeon; if not, take a boat to the jetty. After lunch, while away the heat of the afternoon lolling in the shade of Kitchener Island, and then, if you have time before your plane or train, head over to the Panorama Bar for an unparalleled view up and down the river and a couple of pre-trip drinks.