I've been to Prague many times and it's a great city to visit (even though I may be slightly biased...).
I agree with what Onda said earlier, especially in the city center. Also, Trdelnik is not a traditional Czech pastry, regardless of how much it's advertised (and they are everywhere!). You'll also see a lot of non-Czech related souvenirs in stores.
I was there a few weeks ago and visited the Clementinum. This has been on my list for a long time and it was well worth the visit. As a bonus to viewing the library, you go to the top of the tower which has great views of Prague. Great history with Tycho Brahe and Kepler. You'll need to get tickets beforehand, which I think open up 2 weeks in advance (and they do sell-out).
A unique sightseeing route through a part of the Clementinum, the former Jesuit college, takes you to the Astronomical Tower and the extension that connects it to the northern wing of the Clementinum complex. Here you will have a guided tour of the Baroque Library, described as the most...
prague.eu
Prague is easy to get around. You can walk the central part in most of one day. I enjoy staying in one of the local neighborhoods, usually Vinohrady (Prague 2). There are lots of local restaurants with many expats. English is very common in Prague these days, so language is not an issue.
If you stay in Vinohrady, it's a short walk to the Zizkov tower. It's an odd piece of architecture, but offers nice views of Prague.
You can also get a multi-day transmit pass for a reasonable price. Last trip we bought a 3 day pass at the airport, but in reality, it didn't pay off since we ended up walking most of the time. Public transport works really well, but if you prefer ride-share, then install the Bolt app (Europe's version of Uber), which is inexpensive to use in Czech.
A hike up to Petrin is nice. You can try taking the funicular, but right now it's under reconstruction. You'll need to check to see when it opens. A nice walk/hike is to go up Petrin and then walk the backside to Strahov monastery, and then you can walk down to Prague Castle.
I will say that 5 days is a lot of Prague. You can see most of it in 2 days, 3 days comfortably. But there are tons of side trips you can make in the city or day trips to other towns. Cesky Krumlov is worth a visit, as is the Sedlec Ossuary in Kutna Hora. I'm not sure how easy either are to visit without a car, since I usually rent a car when traveling outside of Prague.
Another less visited place in Prague is Vysehrad, where I'd recommend visiting the cemetery. A number of notable people are buried there.
en.wikipedia.org
As for food, I would recommend trying Tankova Plzen (Plzen poured from a tank). I usually go to a Lokal restaurant (it's a local chain), which has good pours, along with a variety of Czech food.
Some Czech food to try: Svickova and Vepro, Knedlo, Zelo (Pork, Dumplings, Cabbage - I prefer red cabbage). The latter can also be found with duck, which is also excellent.
You should also try a kolac. I can recommend Kus Kolace in Vinohrady. They have more options, but their kolace are excellent.
If you have any questions, feel free to ask.
Note that October can be a little chilly. Definitely bring layers and be prepared for mixed weather.
Have fun!