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I'm trying to learn this song in piano:

What does /5+ or /5- means?

Example: Abm6/5+

Does it mean bass is the fifth augmented?

So in Abm6/5+ does 5+ means the bass is the E note?

Also what the degree symbol means? Example: Ab°

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Based on the tabs you have included it seems the person notating messed up some of the chord notation. In general, a plus sign will mean a raised interval and a minus sign will mean a minor chord or a lowered interval. The slash is supposed to be for notating bass notes, but '5+' is not a note and the bass note given is Ab the root. There is a raised (augmented) 5th in the chord so they probably just got confused with the notation. Based on the notes given a better name for it would have been Abm6(+5) or Abm6(#5). The degrees symbol signifies a diminished chord which is a minor chord with a lowered (diminished) 5th.

Here is a link with more common chord symbols if you are curious about other chords.

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tl;dr: The /5+ is an instruction to play the chord with an augmented fifth instead of a perfect one; the degrees symbol means a diminished chord

As per the tabs (and knowing this song and having played it before), this is an overcomplicated notation for E(b9)/G# (E major with added minor ninth and G# in the bass). See: the Abm6/5+ is Ab-Cb-E-F. Enharmonically, G#-B-E-F. I say Abm6/5+ is overly complicated because E7 (inverted or not) is the dominant (has natural relation with) of Am, while the former does not belong to the harmonic field of Am (G# is the major seventh of A, while Ab is a diminished octave -- tricky).

The degrees symbol represents a diminished seventh chord (not to be confused with the diminished triad).

P.S.: this song is not in F major (A minor is more adequate) and the chords are messed up; I would rather recommend you to follow these chords. Good luck with Bossa Nova!

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Note: E(b9)/G# can also be spelled as G#°(b13) which results in almost the same chord, but even more adequate, as it adds the D note (seventh to the E major chord) and gives more of the required dominant character to such chord (E7(b9)/G#, then). – SeuMenezes Jan 28 '14 at 22:06
so /5+ has nothing to do with the bass? also if (b9) means minor ninth, why the b? – carlosdubusm Jan 29 '14 at 18:00
exactly. this notation with a slash is also dubious. A more convenient notation would use parentheses: Abm6(b5), as a slash is commonly used to indicate bass alterations. By the way, (b5) is a diminished fifth and (b9) is a minor ninth, because by default numbers indicate major intervals -- (9) is major ninth, (5) is perfect fifth. Using the "b" means to lower said interval. In the standard USA chord notation, you can also use a minus sign (5- or 9-). – SeuMenezes Jan 30 '14 at 18:43

Some notation has the - meaning minor chord. Other notation school has - meaning diminished 5th. In that latter school + means an augmented 5th.

Abm6/+5 is Abm6(+5) or: A flat minor 6 with an augmented 5th :-)

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