Helen,does 5 days = 5 full days, not including arrival/departure? Often arrival day is just half a day, and u cannot really count departure day. And if it is 5 FULL days, how much time do you want/need for famous Athens landmarks? I think you really need 2 full & rather long days for that --
(Day 1) early start: Acropolis gate at 8 am to beat the tour-group & cruise crowds, leave 10 am, go thru Ancient Agora... lunch @Acropollis museum 12- 3 pm then NAP? maybe visit other sites (Temple of Zeus, Hadrians arch etc), & dinner &collapse
(2) Nat. Arch museum 3 hrs - lunch.. other sights in aft --specialty museums? Pnyx? wandering Plaka etc; sunset dinner
OUTSIDE ATHENS --
Delphi -- In my experience, tour bus day trips can be disappointing because you show up 8 am then bus takes at least 30 mins to pick up passengers at hotels, then takes until 11 am (with a rest stop) to reach site, you get herded around for an hour, with other crowds, then all jam into the museum at once, then your leader drags you away before 1 pm to the bus for group lunch (which YOU pay for) at a mediocre taverna (kickback??), then to a souvenir store (kickback???), then back to ATHENS & driving round to hotels to drop people off. I so hated this experience that it wasn't until 5 Greece visits later, that I returned to Delphi, using public bus. I stayed o'night & had a radically different experience. Glorious. YOU also can do a satisfying day trip via public bus if you catch the very earliest bus (7:30 am) up & latest one back (6:30?pm)... if this is of interest I can supply details -- advantage is you aren't herded around, & forced to leave -- disadvantage is u need to do some "homework" to appreciate... tho you can hire a fab licensed guide to meet u at the site... standard guide fee for about 2.5 hour tour of site & museum is $170 USD for up to 10 people... if "we" means 4 people, not so much, if "we" means 2, that's costly.
ANOTHER OPTION -- You could upon landing (if you land before noon), rent a car and drive directly from Airport on modern roads, to Delphi, arrive late afternoon, see museum enjoy sunset dinner looking down mountain, Day #2 - visit ancient site early in AM & beat the bus crowds .... then drive on to another wonderful experience, on modern roads -- NAFPLIO. You could stop at Mycenae OR Tiryns OR Nemea on the way, in afternoon enjoy THE most beautiful "Old Town" in all of Greece and a glorious seafront sunset. Next AM (Day #3) visit Epidaurus en route back to Athens. Drop car @ airport (do NOT drive in Athens), taxi (flat rate €38)to a central hotel, put your feet up, have dinner & an early night & do your 2 Athens days last.... after 3 days "in country" the Athens sights will resonate even more.