If you have a 5 V DC power supply connected to a 1Ω resistor and a coil with negligible resistance in series, then you will draw 5 A, and dissipate 25 W in the resistor.
You will need a 1Ω resistor that's capable of dissipating 25 watts. Such a resistor will be physically much, much larger than the typical 1/4 watt resistors you use on circuit boards. In catalogues, they will be called 'Power Resistors'. There are several ways to lose this power. Some types are designed to be used in free air and run very hot, cooled by natural convection. Some must be bolted to a heatsink.
By Dmitry G - Own work, Public Domain, https://commons.wikimedia.org/w/index.php?curid=9806443
For instance, the above resistor is designed for 12 watts in free air, the hand gives you a reference for the size.