Will I have any transport problems considering it will be on a Sunday morning in August?
Five hour is plenty to get to the S-Bahn go to the main train station (Frankfurt am main Hauptbahnhof) get a grab and return to Frankfurt airport. The subway (S-bahn) goes every 15 mins between the city and the airport. But going towards the central attractions is possible but you might have to hurry a little.
But do note that on Sundays (except for verkaufsoffene-sonntag), the shops will be mostly closed in Frankfurt city and there's little you can do there.
Also, do note that it's advisable to reach the airport 2-3 hours before (especially when you're traveling out of the schengen states) so effectively you have around 1-2 hours for travel + food around the Hbf. There's quite a variety of food around the Hbf.
If you're taking the Lufhansa bus, it's not exactly at the airport but at the Squaire building near the conference hall. So do take into account another 10-15 walk to and from the Squaire to the S-bahn station.
Will I be able to leave my luggage somewhere in the airport? (Or quite possibly in Frankfurt Hbf?)
Luggage storage is available http://www.frankfurt-airport.com/content/frankfurt_airport/en/checkin_luggage/luggage_neu/storage.html
And there are also quite a lot of coin-operated lockers at the Hbf too.