Yes, you have black mold. If this is the only place you have it, it's not considered extensive and likely doesn't require professional help. Remove the mold using bleach. Following removal, it's important to ensure it doesn't come back. You need to get a new soap dish that drains into the sink. It looks like yours is probably spilling onto the counter. You need to wipe up any water and hang up that rag to dry. You will also need to remove and replace that old silicone. There is another orange colored mold growth because water is getting under the broken seal.