Answer
Base five Numeral is \[{{12344}_{\text{five}}}\]
Work Step by Step
First write the given Roman numeral as Hindu Arabian Numeral
CMLXXIV\[\,=\left( 1000-100 \right)+\left( 50+10 \right)+10+\left( 5-1 \right)=974\]
Now let’s find out the base five numeral using base ten Hindu Arabic numeral,
The Place values in base five numeral are \[{{5}^{1}},\,{{5}^{2}},{{5}^{3}},{{5}^{4}},\ldots \] or \[5,25,125,625,\ldots \]
Using highest divisor from these place values which is less than dividend for the first time and then continue in same manner, we get
\[\begin{align}
974=625\overset{1}{\overline{\left){974}\right.}} & \\
\underline{625} & \\
349 & \\
\end{align}\]
Then,
\[\begin{align}
125\overset{2}{\overline{\left){349}\right.}} & \\
\underline{250} & \\
99 & \\
\end{align}\]
Then,
\[\begin{align}
25\overset{3}{\overline{\left){99}\right.}} & \\
\underline{75} & \\
24 & \\
\end{align}\]
Then,
\[\begin{align}
245\overset{4}{\overline{\left){24}\right.}} & \\
\underline{20} & \\
4 & \\
\end{align}\]
So,
${{974}_{\text{ten}}}=\,{{12344}_{\text{five}}}$
Using the four quotients and the last remainder, we can directly write the Base Five Numeral as above.