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Nearly 30,000 late-type main-sequence stars with stellar age from LAMOST DR5

We construct a sample of nearly 30,000 main-sequence stars with 4500K $<T\rm_{eff}<$ 5000K and stellar ages estimated by the chromospheric activity$-$age relation. This sample is used to determine the age distribution in the $R-Z$ plane of the Galaxy, where $R$ is the projected Galactocentric distance in the disk midplane and $Z$ is the height above the disk midplane. As $|Z|$ increases, the percentage of old stars becomes larger. It is known that scale-height of Galactic disk increases as $R$ increases, which is called flare. A mild flare from $R$ $\sim$ 8.0 to 9.0 kpc in stellar age distribution is found. We also find that the velocity dispersion increases with age as confirmed by previous studies. Finally we present spiral-shaped structures in $Z-\upsilon_{Z}$ phase space in three stellar age bins. The spiral is clearly seen in the age bin of [0, 1] Gyr, which suggests that a vertical perturbation to the disk probably took place within the last $\sim$ 1.0 Gyr.