Is there a "between" function in C#?

No, but you can write your own:

public static bool Between(this int num, int lower, int upper, bool inclusive = false)
{
    return inclusive
        ? lower <= num && num <= upper
        : lower < num && num < upper;
}

It isn't clear what you mean by "one operation", but no, there's no operator / framework method that I know of to determine if an item is within a range.

You could of course write an extension-method yourself. For example, here's one that assumes that the interval is closed on both end-points.

public static bool IsBetween<T>(this T item, T start, T end)
{
    return Comparer<T>.Default.Compare(item, start) >= 0
        && Comparer<T>.Default.Compare(item, end) <= 0;
}

And then use it as:

bool b = 5.IsBetween(0, 10); // true

Here's a complete class.

/// <summary>
/// An extension class for the between operation
/// name pattern IsBetweenXX where X = I -> Inclusive, X = E -> Exclusive
/// <a href="https://stackoverflow.com/a/13470099/37055"></a>
/// </summary>
public static class BetweenExtensions
{

    /// <summary>
    /// Between check <![CDATA[min <= value <= max]]> 
    /// </summary>
    /// <typeparam name="T"></typeparam>
    /// <param name="value">the value to check</param>
    /// <param name="min">Inclusive minimum border</param>
    /// <param name="max">Inclusive maximum border</param>
    /// <returns>return true if the value is between the min & max else false</returns>
    public static bool IsBetweenII<T>(this T value, T min, T max) where T:IComparable<T>
    {
        return (min.CompareTo(value) <= 0) && (value.CompareTo(max) <= 0);
    }

    /// <summary>
    /// Between check <![CDATA[min < value <= max]]>
    /// </summary>
    /// <typeparam name="T"></typeparam>
    /// <param name="value">the value to check</param>
    /// <param name="min">Exclusive minimum border</param>
    /// <param name="max">Inclusive maximum border</param>
    /// <returns>return true if the value is between the min & max else false</returns>
    public static bool IsBetweenEI<T>(this T value, T min, T max) where T:IComparable<T>
    {
        return (min.CompareTo(value) < 0) && (value.CompareTo(max) <= 0);
    }

    /// <summary>
    /// between check <![CDATA[min <= value < max]]>
    /// </summary>
    /// <typeparam name="T"></typeparam>
    /// <param name="value">the value to check</param>
    /// <param name="min">Inclusive minimum border</param>
    /// <param name="max">Exclusive maximum border</param>
    /// <returns>return true if the value is between the min & max else false</returns>
    public static bool IsBetweenIE<T>(this T value, T min, T max) where T:IComparable<T>
    {
        return (min.CompareTo(value) <= 0) && (value.CompareTo(max) < 0);
    }

    /// <summary>
    /// between check <![CDATA[min < value < max]]>
    /// </summary>
    /// <typeparam name="T"></typeparam>
    /// <param name="value">the value to check</param>
    /// <param name="min">Exclusive minimum border</param>
    /// <param name="max">Exclusive maximum border</param>
    /// <returns>return true if the value is between the min & max else false</returns>

    public static bool IsBetweenEE<T>(this T value, T min, T max) where T:IComparable<T>
    {
        return (min.CompareTo(value) < 0) && (value.CompareTo(max) < 0);
    }
}

plus some unit test code

[TestClass]
public class UnitTest1
{
    [TestMethod]
    public void TestMethodIsBeetween()
    {
        Assert.IsTrue(5.0.IsBetweenII(5.0, 5.0));
        Assert.IsFalse(5.0.IsBetweenEI(5.0, 5.0));
        Assert.IsFalse(5.0.IsBetweenIE(5.0, 5.0));
        Assert.IsFalse(5.0.IsBetweenEE(5.0, 5.0));

        Assert.IsTrue(5.0.IsBetweenII(4.9, 5.0));
        Assert.IsTrue(5.0.IsBetweenEI(4.9, 5.0));
        Assert.IsFalse(5.0.IsBetweenIE(4.9, 5.0));
        Assert.IsFalse(5.0.IsBetweenEE(4.9, 5.0));

        Assert.IsTrue(5.0.IsBetweenII(5.0, 5.1));
        Assert.IsFalse(5.0.IsBetweenEI(5.0, 5.1));
        Assert.IsTrue(5.0.IsBetweenIE(5.0, 5.1));
        Assert.IsFalse(5.0.IsBetweenEE(5.0, 5.1));

        Assert.IsTrue(5.0.IsBetweenII(4.9, 5.1));
        Assert.IsTrue(5.0.IsBetweenEI(4.9, 5.1));
        Assert.IsTrue(5.0.IsBetweenIE(4.9, 5.1));
        Assert.IsTrue(5.0.IsBetweenEE(4.9, 5.1));

        Assert.IsFalse(5.0.IsBetweenII(5.1, 4.9));
        Assert.IsFalse(5.0.IsBetweenEI(5.1, 4.9));
        Assert.IsFalse(5.0.IsBetweenIE(5.1, 4.9));
        Assert.IsFalse(5.0.IsBetweenEE(5.1, 4.9));

    }
}