tcolorbox incompatibe with color package?

xcolor is an enhanced version of color but the real trick here is simply to load it first:

\documentclass{article}
\usepackage[usenames,dvipsnames]{xcolor}
\usepackage{tcolorbox}
\usepackage{lipsum}


\begin{document}

\begin{tcolorbox}[colback=green!5,colframe=green!40!black,title=A nice heading]
\lipsum[2]
\end{tcolorbox}

\end{document}

tcolorbox loads pgf which loads xcolor without options. If you want to pass some options to xcolor (which completely integrates color functionality) you can use cfr solution \usepackage[]{xcolor} with specific options before loading tcolorbox, but you also have two more options.

The first one would be to use \PassOptionsToPackage{usenames,dvipsnames}{xcolor} which passes options usenames and dvipsnames whenever xcolor is loaded.

\PassOptionsToPackage{usenames,dvipsnames}{xcolor}
\documentclass{article}
\usepackage{tcolorbox}
\usepackage{lipsum}

\begin{document}

\begin{tcolorbox}[colback=JungleGreen!5, colframe=JungleGreen!40!black, title=A nice heading]
\lipsum[2]
\end{tcolorbox}

\end{document}

And a second one consists in passing these options through \documentclass because from page 17 in LaTeX Companion, 2ed:

All options to \documentclass (both declared and global ones) are automatically passed as class options to all \usepackage declarations. Thus, if a package file loaded with a \usepackage declaration recognizes (i.e. declares) some of the class options, it can take appropriate actions. If not, the class options will be ignores while processing that package.

As a simple test, I've changed green to JungleGreen (in dvipsnames list) in your example and tried with

\documentclass[dvipsnames]{article} %<--- usenames is an obsolete option. deleted.
\usepackage{tcolorbox}
\usepackage{lipsum}

\begin{document}

\begin{tcolorbox}[colback=JungleGreen!5, colframe=JungleGreen!40!black, title=A nice heading]
\lipsum[2]
\end{tcolorbox}

\end{document}

which works without problems: