1000:5 current transformer: how to calculate burden resistor?
This CT cannot directly output 5V and maintain rated accuracy.  

You need a signal conditioning circuit if you want to get a DC signal suitable to input to an Arduino. 

The maximum VA for rated accuracy is 5, so the maximum burden resistor is 0.2\$\Omega\$ (5W) and therefore the output voltage will be 2.8V P-P (at 1kA AC into a 1-turn primary).