  Let $\ell$ and $r$ be integers. A real number $\alpha \in [0,1)$ is a jump
for $r$ if for any $\varepsilon > 0$ and any integer $m,\ m \geq r$, any
$r$-uniform graph with $n > n_0(\varepsilon,m)$ vertices and at least \alpha+
\varepsilon)\binom{n}{r}$ edges contains a subgraph with $m$ vertices and at
least $(\alpha +c)\binom{m}{r}$ edges, where $c=c(\alpha)$ does not depend on
$\varepsilon$ and $m$. It follows from a theorem of Erd\H{o}s, Stone and
Simonovits that every $\alpha \in [0,1)$ is a jump for $r=2$. Erd\H{o}s asked
whether the same is true for $r \geq 3$. However, Frankl and R\"{o}dl gave a
negative answer by showing that $1-\frac{1}{\ell^{r-1}}$ is not a jump for $r$
if $r \geq 3$ and $\ell >2r$. Peng gave more sequences of non-jumping numbers
for $r=4$ and $r\geq 3$. However, there are also a lot of unknowns on
determining whether a number is a jump for $r \geq 3$. Following a similar
approach as that of Frankl and R\"{o}dl, we give several sequences of
non-jumping numbers for $r=5$, and extend one of the results to every $r \geq
5$, which generalize the above results.
