Can Bencodes Be Described With a Context-Free Grammar?
The language of valid Bencoded values is not context-free&mdash;and nor is just the language of Bencoded strings. Let $L$ be the set of valid Bencoded values, and let $L&#39;$ be the intersection of $L$ with the regular language [0-9]*:a*, i.e. the Bencoded strings with just the symbol a. If $L$ were context-free, so would $L&#39;$, but $L&#39;$ does not satisfy the pumping lemma.

Suppose $L&#39;$ is context-free, the pumping lemma applies. Let $n$ be the pumping threshold and let $w = \mathrm{dec}(n):a^n$, where $\mathrm{dec}(n)$ denotes $n$ written in decimal. Then $w = \alpha\beta\gamma\delta\epsilon$, and $\alpha\beta^m\gamma\delta^m\epsilon \in L&#39;$ for all $m$. The colon must appear in $\gamma$ (the other cases can easily contradicted). Then the number to the left of the colon grows exponentially in $m$ (since its length in decimal increases linearly), but the string to the right only grows linearly, so the number can't be equal to its length.

You said


  If you have a trivial function that converts the ASCII “5” into a unary value and all the other ASCII characters into a character then you have an equivalent structure.


but it turns out that this function is not trivial from the perspective of context-free grammars.