My husband and I are planning a trip to Sarajevo for next April/May and the best flight has a layover of five hours in the morning in Vienna. Is this enough time to go into the city and see any of it or get breakfast? We have never been there, and it seems like a great opportunity if it's possible. Thank you.

With only 5 hrs I wouldn't chance it. If you haven't booked your flight yet, why don't you change it and stay for at least a couple of days.

When your incoming flight is on time, it's doable but probably not too enjoyable.
What Bedar suggests makes more sense.
Most booking engines let you play with layover times.

Five hours really isn't sufficient for a quick visit to Vienna. The airport is about 20km from the center of the city; catching even the express train (€17 RT, every 30 minutes) and then the U-Bahn to Stephansdom, for example could eat more than an hour of that time. Time to get through security on the return would need to be factored, as well. Finally, depending on the time of day, and the day, you would arrive, there might not be more than a bakery open once you did reach the city.

You might also want to note the layover hours (e.g. the time of day) you have at VIE; though it's an international airport, its offerings are limited and boredom can set in early.

Thanks so much for your advice. I found some similar questions about layovers in Vienna from 2006 and 2007, and some replies were for it and some against. I didn't know if things have changed since then. It would make me nervous to leave the airport, but it was tempting.