Q: Is there a sixth sense according to science? 

Krishna: People usually recognize five senses: taste, smell, vision, hearing, and touch.

Right! If you ask a person to close his eyes and touch his right foot with his left hand, he would without seeing it, hearing it make noise, smelling it or tasting it and perhaps even without touching it before actually  touching it! This sense of your own body, its position and its movement is called “proprioception.”

This sense of your own body, its position and its movement is called “proprioception.”Proprioception, otherwise known as kinesthesia, is your body's ability to sense movement, action, and location. It's present in every muscle movement you have. Without proprioception, you wouldn't be able to move without thinking about your next step. This is what we think when you ask about sixth sense.

However, Intuition, or the Sixth Sense, involves unconscious decision-making based on patterns and prior experiences, according to some people. This intuition is a cognitive process operating through thin-slicing and processing vast amounts of information from memory and pattern recognition. Intuition can guide decision-making, problem-solving, relationship assessment, and personal safety and well-being.

The brain, through a complex array of neural circuits, is something of a statistical inferencing machine.

The “highest” level of cognition, and the level possibly unique to humans, is the capacity for critical thinking using data and fact based knowledge. 

The “lowest” levels of behaviour are hard-wired reflexes and adaptive “conditioned responses,” for example avoiding foods that previously made you sick.

Somewhere in between is a complex system located in the central region of the brain called the “basal ganglia” that is responsible for “habit formation”, and which is also likely responsible for what we call intuition.

Intuition  means an accumulation of attitudes (including beliefs and opinions) derived from experience, both individual and cultural. It is closely associated with some prior knowledge, which forms the basis of intuition.

However, at least one type of "sixth sense" isn't real, research suggests (1). It found that what people perceive as a sixth sense may simply be their vision systems detecting changes they can't articulate.
People can sense things that they believe they cannot see such as changes in a person's appearance. But this isn't anything magical or a sixth sense; this can be explained in terms of known visual processing.
While a few scientific studies have hinted that people can sense the future just before it happens, follow-up studies concluded these results were artifacts of statistics or flawed study design.
The findings suggest the origin of the phenomenon in which a person seems to be intuitively aware of something that they don't believe they have seen or sensed in another way is due to the perception of differences in the visual metrics, not a sense that operates outside the normal laws of physics. For instance, in the case of a person who might  have noticed tiny changes in somebody's appearance (such as small cuts or a bandage), but not been consciously aware that they picked up on those cues.
For those who think that they have a sixth sense, however, it's a very compelling feeling that they have a sensing ability. And you do have a sensing ability — it's just not magical, it is just plain ability that came from a normal sense without your knowledge!

Intuition — the idea that individuals can make successful decisions without deliberate analytical thought — has intrigued philosophers and scientists since at least the times of the ancient Greeks. But scientists have had trouble finding quantifiable evidence that intuition actually exists.

Some research (2) suggests that  we can use unconscious information in our body or brain to help guide us through life, to enable better decisions, faster decisions, and be more confident in the decisions we make. Researchers found that people were able to make faster and more accurate decisions when they unconsciously viewed some emotional images. Essentially, people’s brains were able to process and utilize information from the images to improve their decisions. Another interesting finding in this study is that intuition improved over time, suggesting that the mechanisms of intuition can be improved with practice. 

So all these studies say intuition doesn't come from no where. Prior knowledge, past experiences, through analysis of something and visual or other cues that people don't consciously notice like sounds, air currents, vibrations felt by the body, variations in light - all of these things  play on our minds to predict something, which we call 'intuition'.  Your subconscious mind uses a whole lot more data than your conscious mind, so things that you aren't consciously aware of can be used to make decisions, and your brain is constantly doing this. Science says  intuitions get better with practice — especially with a lot of practice — because at bottom intuition is about the brain’s ability to pick up on certain recurring patterns; the more we are exposed to a particular domain of activity the more familiar we become with the relevant patterns (charts, positions of chess pieces), and the more and faster our brains generate heuristic solutions to the problem we happen to be facing within that domain.

Educated guess work? Informed imagination? Without your full knowledge? Maybe!

The word intuition comes from the Latin intuir, which appropriately means ‘knowledge from within.’ 

Intuition works in an associative manner: it feels effortless (even though it does use a significant amount of brain power), and it’s fast. Rational thinking, on the contrary, is analytical, requires effort, and is slow. Why, then, would we ever want to use a system that makes us work hard and doesn't deliver rapid results? Think of it this way: intuitions, contrary to much popular lore, are not infallible. Cognitive scientists treat them as quick first assessments of a given situation, as provisional hypotheses in need of further checking.

“Intuition” can be roughly understood as the brain’s ability to form probabilistic assumptions automatically, without us having much introspective insight into the process the brain is using. This is called as sixth sense by some. 

Scientists don't recommend it because you need to be willing to take risks and be wrong from time to time if you go the intuition way. Critical thinking is the best option, even if you have to put in more effort.

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