time to fist byte (TFB) is extremely bad

hello!

i would be very grateful if somebody could help me with this problem:

the website http://www.extrarot.com is hosted on a very good & fast server (wpengine), which does good caching for not logged in users as well.
i know that there are many things which should be optimized (like css, scripts,…), but one problem is the worst: the time to fist byte (TFB).
it takes at least 5 seconds, until the first byte is sent.

css should not be the problem, because these things do not influence TFB.
and i checked for connections to – for example – twitter or other sites, which might cause the problem, but did not find anything.

does anybody know how to fix this problem?
is it possible, that s2member slows down a website so much?

thanks for help in advance!
best regards, roland