It's a bad bug indeed in the metrics for TeX Gyre Termes. Note that the same happens with the OpenType version. And also with newtxtext
(that uses a different clone of Times New Roman)
You can at least obviate to the problem by redefining \labelitemii
:
\documentclass{article}
\usepackage{tgtermes}
\renewcommand{\labelenumii}{(\theenumii\/)} % add the italic correction
\begin{document}
\begin{enumerate}
\item \begin{enumerate}% go to the second level
\setcounter{enumii}{5}% print just the f item
\item x
\end{enumerate}
\end{enumerate}
\end{document}

It's a fact that all clones of Times New Roman available in TeX distributions exhibit the same problem. In the TFM files for Computer Modern we find (abridged version)
(LIGTABLE
(LABEL C f)
(KRN O 51 R 0.077779)
which means that Computer Modern applies a small kerning between an “f” and a closed parenthesis (ASCII octal '51).
The rm-qtmr
font (TeX Gyre Termes under OT1 encoding, but it's the same for ec-qtmr
, used for the T1 encoding) has an extensive kerning table for “f”, but misses the closed parenthesis.
The same happens with the fonts used by newtxtext
and by mathptmx
.
This bug should be made known to the maintainers of the font packages. In the case of Computer Modern the kerning is small, because the drop of the “f” is not so much outside the bounding box. A larger kerning is needed with Times New Roman, where the drop protrudes more, but the fonts define none.