Mesh Analysis with a Current sources and current direction
This question is basically testing whether you can step back from your intuitive understanding of how circuits behave and just apply the mathematical rules you've learned. 

For example, you're going to find that at least one of the unknown resistors must have a negative value for the given resistances and currents to be correct. 

That's okay. In some circuit simulations negative resistors will appear and you will have to be prepared to accept them and just get on with solving the circuit. 


  My first question is how is the current 10 A flowing towards the voltage source?


It couldn't if there were no other power sources in the circuit besides the 5 A current source and 50 V voltage source. 

But negative-value resistors can also deliver power to a circuit. 


  Second question is if I were to do a mesh analysis on 3 loops going in a clock wise direction should the left most loop with the current source just have an equation where current i going around in a clockwise direction just simply set to 5A?


You could set up a mesh equation, but you'd immediately set the current of that mesh to 5 A (assuming you use clockwise mesh current convention). So it amounts to the same thing.


  which would make \$i_2=−3\$?


Yes, By KCL \$i_2\$ must be -3 A. Which is also counter-intuitive if you assume all resistors have positive values.

Nonetheless you can continue to use the rules you know (KCL and KVL) to find all the unknown currents and voltages in this circuit.