For every positive integer $n$, let ${\text{mod}}_7(n)$ be the remainder obtained when $n$ is divided by 7. Define a function $g:0,1,2,3,\dots \times 0,1,2,3,4,5,6\to 0,1,2,3,4,5,6$ recursively as follows:
$g(i,j)=\{\begin{array}{ll}{\text{mod}}_7(j+2)& \text{if }i=0\text{ and }0\le j\le 6,\\ g(i-1,2)& \text{if }i\ge 1\text{ and }j=0,\\ g(i-1,g(i,j-1))& \text{if }i\ge 1\text{ and }1\le j\le 6.\end{array}$
What is $g(2023,5)$?