Let
M
M
be a 5-dimensional Riemannian manifold with
S
e
c
M
∈
[
0
,
1
]
Sec_M\in [0,1]
and
Σ
\Sigma
be a locally conformally flat closed hypersurface in
M
M
with mean curvature function
H
H
. We prove that there exists
ε
0
>
0
\varepsilon _0>0
such that
∫
Σ
(
1
+
H
2
)
2
≥
4
π
2
3
χ
(
Σ
)
,
\begin{align} \int _\Sigma (1+H^2)^2 \ge \frac {4\pi ^2}{3}\chi (\Sigma ), \end{align}
provided
|
H
|
≤
ε
0
\vert H\vert \le \varepsilon _0
, where
χ
(
Σ
)
\chi (\Sigma )
is the Euler number of
Σ
\Sigma
. In particular, if
Σ
\Sigma
is a locally conformally flat minimal hypersphere in
M
M
, then
V
o
l
(
Σ
)
≥
8
π
2
/
3
Vol(\Sigma ) \ge 8\pi ^2/3
, which partially answers a question proposed by Mazet and Rosenberg. Moreover, we show that if
M
M
is (some special but large class) rotationally symmetric, then the inequality (\ref{V1}) holds for all
H
H
.