Hydrolysing large molecules to reveal amino acids
You are on the right track.  $\ce{NH_2-C(H)R-COOH}$ is the formula for an alpha amino acid, one where the amino group of the molecule is attached to a carbon atom one carbon atom away from the carboxylate carbon.  This is the most common type of amino acid found in biochemistry.  (A beta amino acid would be $\ce{NH_2-C(H)R^2-C(H)R^1-COOH}$).

When amino acids condense into a polymer or oligomer they do so by forming peptide bonds, also called amide bonds.  

$\ce{R^1COOH + NH2R^2 -&gt; R^1CONH2R^2 + H2O}$

So to find the places in oxytocin that would be hyrolyzed into amino acids, look for individual carbon atoms that are attached to both (i) an oxygen atom via a double bond and (ii) a nitrogen atom while (iii) not being attached to any other heteroatoms.  (Item (iii) is generally necessary to exclude other functional groups such as carbamides or carbamates, but these groups are not found in oxytocin.)  For oxytocin, your impulse to look just at carbon double-bonded to oxygen (item (i) only) is OK, but be warned that this procedure is not precise enough in general, because molecules with e.g. ketone moieties will have C=O bonds but will not be hydrolyzed.

The red-circled amino group is a free amino group:  the carbon attached to it is not bound to a carbonyl oxygen, so it is not a place where hydrolysis will happen.  (However, look one carbon atom to the left of C atom attached to the circled N....)

@DavePhD is right; there are more than five amide bonds in oxytocin.  I think there are a total of ten.  Eight are the result of amide bond formation between alpha amino acids and two are the result of amide bond formation between an acid side chain and unsubstituted ammonia.