Override the numbers in an algorithm

Question

I have tried a few ways I found here, including This, and This, there are more but I can't remember them.

The issue I'm having is I'd like "Fifth Instruction" to start on 5, I know "Third Instruction" has the correct number by accident, but none of my attempts seem to work. I'm happy with the indented sections being automatically renumbered, but even if it was one numbering the whole way down (1-13) but indented I'd be happy – I can't seem to manage that either.

Any help is really appreciated!

\usepackage{algorithm,algpseudocode}
\usepackage{algorithm2e}
\begin{document}
\begin{algorithm}
\begin{algorithmic}[1]
\State First Instruction
\State Second Instruction
\begin{algorithmic}[1]
     \State Instruction 2.1
     \State Instruction 2.2
\end{algorithmic}\\
Third Instruction\\
Fourth Instruction
\begin{algorithmic}[1]
     \State Instruction 4.1
     \State Instruction 4.2
     \State Instruction 4.3
\end{algorithmic}\\
Fifth Instruction
\begin{algorithmic}[1]
     \State Instruction 5.1
     \State Instruction 5.2
\end{algorithmic}\\
Instruction 6
\end{algorithmic}
\end{algorithm}

Answer 1

A simple way with continuous numbering is to use extra indents with \hspace. To be consistent with the default indentation of algorithmic you can use \algorithmicindent as the value for the extra indent (this is 1.5em by default).

MWE (note that I removed algorithm2e because it was causing an error):

\documentclass{article}
\usepackage{algorithm,algpseudocode}
\begin{document}
\begin{algorithm}
\begin{algorithmic}[1]
\State First Instruction
\State Second Instruction
     \State\hspace{\algorithmicindent} Instruction 2.1
     \State\hspace{\algorithmicindent} Instruction 2.2
\State Third Instruction
\State Fourth Instruction
     \State\hspace{\algorithmicindent} Instruction 4.1
     \State\hspace{\algorithmicindent} Instruction 4.2
     \State\hspace{\algorithmicindent} Instruction 4.3
\State Fifth Instruction
     \State\hspace{\algorithmicindent} Instruction 5.1
     \State\hspace{\algorithmicindent} Instruction 5.2
\State Instruction 6
\end{algorithmic}
\end{algorithm}
\end{document}

Result: