Making latex multicolumn width wider in Rmarkdown - r

Question

I want to make my LaTeX table (picture below) in Rmarkdown to the full width(so that it fits the caption), which requires the 2ndto 5th columns to be extended. I went through multiple links(one,two) but failed. How can I make the table to the full width, and if the columns 2- have the same width, it would be better.
Here is the code
Preamble:
---
title: "misc"
author: "Me"
date: "`r Sys.Date()`"
output:
pdf_document:
keep_tex: true
extra_dependencies: caption
number_sections: yes
fig_caption: yes
classoption: table
header-includes:
- \usepackage{color}
- \usepackage{xcolor}
- \usepackage{float}
- \usepackage{framed}
- \usepackage{fontawesome}
- \usepackage{caption}
- \usepackage{multirow}
- \usepackage{caption}
- \usepackage{tabularx}
- \usepackage{array}
language:
label:
fig: !expr function(x) sprintf("**Figure %s.** ", x)
fontsize: 11pt
urlcolor: blue
---
LaTeX:
\begin{table}[h!]
\centering
\caption[Transformation table]{Transformations generated by Mach et al. Y in a dark cell: highly recommended, Y in a light cell: usable, N in a dark cell: unusable \label{tab:power}}
\begin{tabular}{|
>{\columncolor[HTML]{656565}}l |lcccc|}
\hline
\multicolumn{1}{|c|}{\cellcolor[HTML]{FFFFFF}{\color[HTML]{FFFFFF} }} & \multicolumn{5}{c|}{\cellcolor[HTML]{656565}{\color[HTML]{FFFFFF} Type of Distribution}} \\ \hline
\cellcolor[HTML]{656565}{\color[HTML]{FFFFFF} } & \multicolumn{1}{l|}{} & \multicolumn{1}{l|}{Lognormal} & \multicolumn{1}{l|}{Exponential} & \multicolumn{1}{l|}{Gamma} & \multicolumn{1}{l|}{Weibull} \\ \cline{2-6}
\cellcolor[HTML]{656565}{\color[HTML]{FFFFFF} } & \multicolumn{1}{l|}{Box-Cox} & \multicolumn{1}{c|}{Y} & \multicolumn{1}{c|}{Y} & \multicolumn{1}{c|}{\cellcolor[HTML]{9B9B9B}\textbf{Y}} & \cellcolor[HTML]{9B9B9B}\textbf{Y} \\ \cline{2-6}
\cellcolor[HTML]{656565}{\color[HTML]{FFFFFF} } & \multicolumn{1}{l|}{Exponential} & \multicolumn{1}{c|}{Y} & \multicolumn{1}{c|}{Y} & \multicolumn{1}{c|}{Y} & Y \\ \cline{2-6}
\cellcolor[HTML]{656565}{\color[HTML]{FFFFFF} } & \multicolumn{1}{l|}{Simple power} & \multicolumn{1}{c|}{Y} & \multicolumn{1}{c|}{\cellcolor[HTML]{9B9B9B}\textbf{Y}} & \multicolumn{1}{c|}{\cellcolor[HTML]{9B9B9B}\textbf{Y}} & \cellcolor[HTML]{9B9B9B}\textbf{Y} \\ \cline{2-6}
\multirow{-5}{*}{\cellcolor[HTML]{656565}{\color[HTML]{FFFFFF} \begin{tabular}[c]{#{}l#{}}Type of Transformation\end{tabular}}} & \multicolumn{1}{l|}{Logarithmic} & \multicolumn{1}{c|}{\cellcolor[HTML]{9B9B9B}\textbf{Y}} & \multicolumn{1}{c|}{Y} & \multicolumn{1}{c|}{\textbf{N}} & \textbf{N} \\ \hline
\end{tabular}
\end{table}
Edited to include the code without markups:
\begin{table}[]
\begin{tabular}{|l|lcccc|}
\hline
\multicolumn{1}{|c|}{} & \multicolumn{5}{c|}{Type of Distribution} \\ \hline
\multirow{5}{*}{\begin{tabular}[c]{#{}l#{}}Type of\\ transformation\end{tabular}} & \multicolumn{1}{l|}{} & \multicolumn{1}{l|}{Lognormal} & \multicolumn{1}{l|}{Exponential} & \multicolumn{1}{l|}{Gamma} & \multicolumn{1}{l|}{Weibull} \\ \cline{2-6}
& \multicolumn{1}{l|}{Box-Cox} & \multicolumn{1}{c|}{Y} & \multicolumn{1}{c|}{Y} & \multicolumn{1}{c|}{\textbf{Y}} & \textbf{Y} \\ \cline{2-6}
& \multicolumn{1}{l|}{Exponential} & \multicolumn{1}{c|}{Y} & \multicolumn{1}{c|}{Y} & \multicolumn{1}{c|}{Y} & Y \\ \cline{2-6}
& \multicolumn{1}{l|}{Simple power} & \multicolumn{1}{c|}{Y} & \multicolumn{1}{c|}{\textbf{Y}} & \multicolumn{1}{c|}{\textbf{Y}} & \textbf{Y} \\ \cline{2-6}
& \multicolumn{1}{l|}{Logarithmic} & \multicolumn{1}{c|}{\textbf{Y}} & \multicolumn{1}{c|}{Y} & \multicolumn{1}{c|}{\textbf{N}} & \textbf{N} \\ \hline
\end{tabular}
\end{table}

Answer 1

As said before, I would use the tabularray package. This will give a much nicer result. No white gaps between cells, better spacing ...
---
title: "misc"
author: "Me"
date: "`r Sys.Date()`"
output:
pdf_document:
keep_tex: true
extra_dependencies: caption
number_sections: yes
fig_caption: yes
classoption: table
header-includes:
- \usepackage{tabularray}
language:
label:
fig: !expr function(x) sprintf("**Figure %s.** ", x)
fontsize: 11pt
urlcolor: blue
---
\begin{table}[h!]
\centering
\caption[Transformation table]{Transformations generated by Mach et al. Y in a dark cell: highly recommended, Y in a light cell: usable, N in a dark cell: unusable \label{tab:power}}
\begin{tblr}{
colspec={XXXXXX},
vlines,
hlines,
cells={halign=c},
column{1-2}={halign=l},
vspan=even,
cell{1}{2}={halign=c,bg=gray,fg=white},
cell{2}{1}={bg=gray,fg=white},
cell{3}{5-6}={bg=lightgray,font=\bfseries},
cell{5}{4-6}={bg=lightgray,font=\bfseries},
cell{6}{3}={bg=lightgray,font=\bfseries},
}
& \SetCell[c=5]{} Type of Distribution & & & &\\
\SetCell[r=5]{} Type of Transformation & & Lognormal & Exponential & Gamma & Weibull \\
& Box-Cox & Y & Y & Y & Y \\
& Exponential & Y & Y & Y & Y\\
& Simple power & Y & Y & Y & Y \\
& Logarithmic & Y & Y & N & N \\
\end{tblr}
\end{table}