Application of Ohm's Law:
\[
V = IR
\]
With:
- Voltage (\( V \)) = 10 V,
- Current (\( I \)) = Unknown,
- Resistance (\( R \)) = 5 ohms.
Formula rearranged to find \( I \):
\[
I = \frac{V}{R}
\]
Value substitution:
\[
I = \frac{10 \, \text{V}}{5 \, \Omega} = 2 \, \text{A}
\]
Therefore, the resistor carries a current of \( 2.0 \, \text{A} \).