[BruceZ]

Each resistor is connected directly across the battery, so all 5 resistors are in parallel. V1 = 32, V2 = 32, I1 = 32/R3. The equivalent resistance is actually Req = R1 || R2 || R3 || R4 || R5 = 1/(1/R1 + 1/R2 + 1/R3 + 1/R4 + 1/R5). I2 = 32/Req.

Electricity doesn't only take the "path of least resistance". It takes all possible paths to ground, with a current in each path in inverse proportion to the resistance of that path.

EDIT: If the voltage source is actually a 32 volt battery with some internal resistance Rint, then compute I2 as 32/(Req+Rint) and scale the voltage across each resistor as 32*Req/(Req + Rint). This would not apply to an idealized 32 volt source, or if the 32 volts refers to the actual voltage across the battery in the circuit.