Ohm's law clarification
You can't specify the current AND the voltage.  Either you are applying 5V or you are applying 1A.  Since you have a batery symbol drawn, I will assume you are applying 5 volts.  

This 5v is applied across two 1 ohm resistors in series.  Total resistance of two 1 ohm resistors in series is 1 + 1 = 2 ohms.  V = I * R tells us that 5 = I * 2 where I = 2.5 A.  Then the voltage across each resistor is V = 2.5 * 1 = 2.5 volts.  

How about applying 1 A to two series 1 ohm resistors?  Well, that 1 A is going to produce V = 1 A * 1 ohm = 1 volt across each resistor.  Since there are two 1 ohm resistors in series, the voltage across the pair is 1 + 1 = 2 volts.  

The current must be the same at all points along that path as charges cannot be created or destroyed ('what goes in must come out').  The voltages around the loop must also add up to zero ('what goes up must come down').  In this case, you go up 5 volts in the battery, then you come down 2.5 volts in each resistor, ending up at zero right where you started.