In your first example, Public Fields versus Automatic Properties is a good answer. Basically, you should use always properties instead of fields for non-private things. This lets you do things like modify the code later without breaking things, and make a private set. Properties can also do things like notify code when they're changed or provide default or calculated values easily. And you can use auto-properties to cut down on extraneous code:
public int CurrentValue { get; set; }
Your second example is not a good use of properties, since it breaks the assumptions of how properties work. E.g. if I set the property to 3 and no exception is thrown, I'd expect it to be 3 when I get it, not 15. currentValue = currentValue * 5;, which could make sense working with a field, property, or local variable, makes the value 5 times larger. Maybe you meant something like this:
int currentBackingValue;
public int CurrentValue
{
get { return currentBackingValue * 5; }
}
Without a set, this can work nicely, and without breaking any conventions and assumptions: CurrentValue is calculated based on currentBackingValue.
(as an aside, you should note that the getters and setters of a property are, in fact, methods, just used with a field-like syntax to replace something like Java's getX/setX standard)