Let $\mathcal{D}$ be the whole space $\mathbb{R}^d$ or a sphere of radius $R>0$ in $\mathbb{R}^d$ with $1\leq d\leq3$. Consider the following cubic-quintic energy functional \begin{gather*} \begin{aligned} E_{N}(φ)=\frac{1}{2}\int_{\mathcal{D}}|\nabla φ|^2\,dx-\frac{N}{4}\int_{ \mathcal{D}}|φ|^{4}\,dx+\frac{N^{2}}{6}\int_{\mathcal{D}}|φ|^6\,dx \end{aligned} \end{gather*} minimized in $\left\lbrace φ\in H^1_0(\mathcal{D}): \int_{\mathcal{D}}|φ|^2\,dx=1\right\rbrace$. Firstly, we prove the limiting behavior of the ground state $φ_N$ as $N\to+\infty$, which corresponds to the \emph{Thomas-Fermi limit}. The limit profile is given by the Thomas-Fermi minimizer $u^{TF}=\sqrt{{3\cdot\mathbb{1}_Ω}/{4}}(x)$ with $Ω=B(0,\sqrt[d]{4/(3ω_d)})$. Moreover, we obtain a sharp vanishing rate for $φ_N$ that $\|φ_{N}\|_{L^\infty(\mathcal{D})}\sim N^{-{1}/{2}}$ as $N\to+\infty$. Finally, we prove that $\left\|N^{{1}/{2}}φ_{N}\left(N^{{1}/{d}}x\right)-u^{TF}(x)\right\|_{L^\infty\left(Ω\right)}\lesssim N^{-1/(2d)}$ as $N\to+\infty$.