If you are in a hurry to sent some coins away and don't want to wait days to resync, you can export you private keys from bitcoin core and import them into a light client such as Electrum or Multibit.
If you really would like to use bitcoin core, you can download a "bootscrap.dat" via bittorrent and import it into bitcoin core. It is usually only 2/3 weeks behind.
The link to the bootstrap.dat torrent is
https://bitcoin.org/bin/blockchain/bootstrap.dat.torrent or you can find it on the bitcoin.org page download page
https://bitcoin.org/en/download.
To find it yourself without trusting these links is to go to the bitcoin home page
https://bitcoin.org/en/, then getting started,choose your wallet,bitcoin core download,bootstrap.dat.