The information limits the choices of amino acids, especially the �?.5 overall charge. From the given information, it can be concluded that,
a) Five different amino acids are present.
b) One or more aromatic R-groups are present (Trp, Tyr, or Phe).
c) Charges of all R-groups plus the C-terminus add up to �?.5.
d) Oxidation of cysteine R–SH –�?gt; cystine R–S–S–R (the decapeptide) + 2 H+ + 2e�?/SUP>
(so cysteine is present).
If the pH is significantly above pKa, then the group will be in its deprotonated form,
(–COOH –�?gt; –COO�?/SUP> and –NH3+ –�?gt; –NH2) with corresponding charges.
Amino Acids with Non-Neutral R-Groups:
Amino Acid Approximate pKa of R-group Charge of R-group at pH 10.5
Asp 3.9 �?
Glu 4.1 �?
Arg 12.5 +1
Lys 10.5 50% +1, 50% 0 (pH = pKa)
His 6.0 0
Cys 8.4 (–SH) �?
Tyr 10.5 50% 0, 50% �? (pH = pKa)
N-terminus pKa = 8.0, charge at pH 10.5 = 0
C-terminus pKa = 3.0, charge at pH 10.5 = �?
At pH 10.5, the following adds up to �?.5:
(C-terminus) �?
Cys �?
Arg +1
Lys +0.5 (50% +1, 50% 0)
Total Charge �?.5
Cysteine is definitely present. The cysteine R-group at pH 10.5 has a �? charge (R–S�?/SUP>). The C-terminus will also be in its COO�?/SUP> form at pH 10.5, so that's another �? charge, bringing the total to �? at this point. To get the charge to �?.5, there is not any choice but to have an arginine with the +1 guanadino group at pH 10.5, which brings the overall charge down to �?, plus a lysine which is 50% protonated (–NH3+) at pH 10.5, netting to a +0.5 charge, which makes the overall charge �?.5.
To bring the total number of amino acids up to five, we need two more with neutral R-groups. One at least of these will contain an aromatic ring, such as phenylalanine or tryptophan, both which absorbs light at 280 nm. Since it states that the peptide strongly absorbs at 280 nm, perhaps both of these are present. Otherwise, I can't tell how to determine what the fifth amino acid is from the given information. 
Steve
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