Trouble with a Classical piece...

Romance Anonimo as arranged by Frederick Noad. I'm find until I get half way down the page to what are likely chords. I'm reading the TAB that shows 8 on the bottom E string and 5 on the top E string. It continues 5 on the second string from the bottom, 5 on the third string from the bottom and changes to 7 on the bottom E string, 5 on the second string from the bottom, 5 on the third string on the bottom. What chords are these? I'm having trouble with the finger placement. It then moves to 7 on the bottom E and top E string 7 on the second from the bottom, 8 on the third from the bottom. I'm assuming these numbers are referring to frets but I'm not sure which fingers I'm supposed to use throughout the piece. Anyone familiar with the arrangement? I'd love to hear from you.

Yep, I know of the song as it's pretty much a classical standard, but I never actually took time to learn it all the way. I'm having a little trouble following your description of the tab too, and which parts you're talking about. My easiest answer is to upgrade to full access for $5, and you can watch the series of in-depth video lessons an instructor did for that song (among others), and watch how he frets it throughout.
Romance Lesson

Oh...forgot to mention, it may not be the exact same arrangement, but it is the same song. For instance, I could tell that your tab tells you to hold the 6th string on A at the 5th fret for the bass...but the lesson here (and in another version I saw) just uses the open A string. Generally I'll prefer to use an open string when possible to let it ring out with more sustain, and it's just plain easier at times.