honestly i think perhaps you should ask on the road cycling forum, b/c this is their thing.

the bike won't matter for such a short distance. i would say drop bars are great allowing you to take a position that increases speed. the tires 700x32 would help. i am used to commuting on 700x25 but was recently persuaded to use 700x28. honestly, i think 700x25 gatorskins are just fine even in pothole-filled NYC if you want speed. the 700x28s don't add any cushion, just slight drag. i don't notice it though and my times are not affected. but i imagine 35 to 28 or 35 to 25 would make a difference.

my commute is 5 miles one way and i was getting faster as i biked more 5x a week both ways. it went from 25 min. to 22. to 19. and now to 17 min. it is all due to repetition and getting comfortable on the ride. once you ride everyday both ways (so (5 x 2 x 5 = 50 miles a week) it will just come naturally.

i also think it's all in the technique for enduring and maintaining speed. also just general traffic awareness. there are times you cannot maintain speed due to traffic, lights. but for the rest of your trip, you can maintain speed.

this article on cadence help me shave those last 2 minutes off: Shifting and Cadence - Bicycle Habitat Women's Cycling going from 19 min to 17 min for 5 miles.

the same article was featured on active.com cycling as well. i highly recommend looking over your position on the bike - make sure your bike fits you at every point, seat post, leg extension thru the stroke and bar throw (how far the bar is). once your confident these are correct, look at your cadence. after that pedal stroke.

a lot of people say clipless is probably not worth it for 5 miles. but i would consider some kind of foot retention. a mountain bike clipless set up would work (recessed clips) b/c you don't have to change out of your shoes. i know someone who uses chrome recessed clipless and swears by it. also, i've been using toe gates for years and i absolutely prefer them to just flat pedals. getting power from your up stroke in addition to your down stroke makes a huge difference.

and shoes. firm shoes are a must. don't ride in running shoes or other soft trainers. i use chrome kursks and they help make pedaling effortless and powerful.