[tex]\bf \begin{cases}
x=5cos(t)\implies \cfrac{x}{5}=cos(t)\\\\
y=5sin(t)\implies \cfrac{y}{5}=sin(t)
\end{cases}
\\\\\\
\textit{now, recall that }sin^2(\theta)+cos^2(\theta)=1\qquad thus
\\\\\\
\left( \cfrac{x}{5} \right)^2+\left( \cfrac{y}{5} \right)^2=1\implies \cfrac{x^2}{5^2}+\cfrac{y^2}{5^2}=1\implies \cfrac{x^2+y^2}{25}=1
\\\\\\
x^2+y^2=25\implies x^2+y^2=5^2\impliedby \textit{which is just a circle}[/tex]
