An object reference is required to access a non-static member

playSound is a static method meaning it exists when the program is loaded. audioSounds and minTime are SoundManager instance variable, meaning they will exist within an instance of SoundManager. You have not created an instance of SoundManager so audioSounds doesn't exist (or it does but you do not have a reference to a SoundManager object to see that).

To solve your problem you can either make audioSounds static:

public static List<AudioSource> audioSounds = new List<AudioSource>();
public static double minTime = 0.5;

so they will be created and may be referenced in the same way that PlaySound will be. Alternatively you can create an instance of SoundManager from within your method:

SoundManager soundManager = new SoundManager();
foreach (AudioSource sound in soundManager.audioSounds) // Loop through List with foreach
{
    if (sourceSound.name != sound.name && sound.time <= soundManager.minTime)
    {
        playsound = true;
    }
}

You should make your audioSounds and minTime members static:

public static List<AudioSource> audioSounds = new List<AudioSource>();
public static double minTime = 0.5;

But I would consider using singleton objects instead of static members instead:

public class SoundManager : MonoBehaviour
{

    public List<AudioSource> audioSounds = new List<AudioSource>();
    public double minTime = 0.5;

    public static SoundManager Instance { get; private set; }

    void Awake()
    {
        Instance = this;
    }

    public void playSound(AudioClip sourceSound, Vector3 objectPosition, int volume, float audioPitch, int dopplerLevel)
    {    
        bool playsound = false;
        foreach (AudioSource sound in audioSounds) // Loop through List with foreach
        {  
            if (sourceSound.name != sound.name && sound.time <= minTime)
            {
                playsound = true;
            }
        }

        if(playsound) {
            AudioSource.PlayClipAtPoint(sourceSound, objectPosition);
        }

    }
}

---

Update from September 2020:

Six years later, it is still one of my most upvoted answers on StackOverflow, so I feel obligated to add: singleton is a pattern that creates a lot of problems down the road, and personally, I consider it to be an anti-pattern. It can be accessed from anywhere, and using singletons for different game systems creates a spaghetti of invisible dependencies between different parts of your project.

If you're just learning to program, using singletons is OK for now. But please, consider reading about Dependency Injection, Inversion of Control and other architectural patterns. At least file it under "stuff I will learn later". This may sound as an overkill when you first learn about them, but a proper architecture can become a life-saver on middle and big projects.

I'm guessing you get the error on accessing audioSounds and minTime, right?

The problem is you can't access instance members from static methods. What this means is that, a static method is a method that exists only once and can be used by all other objects (if its access modifier permits it).

Instance members, on the other hand, are created for every instance of the object. So if you create ten instances, how would the runtime know out of all these instances, which audioSounds list it should access?

Like others said, make your audioSounds and minTime static, or you could make your method an instance method, if your design permits it.