If I am decelarating forwards am I accelerating backwards? If I am in a car and I put the brakes on so that I am slowing down (decelerating) am I then accelerating backwards? e.g. If I am decelerating in this car at -5ms⁻² am I accelerating backwards at 5ms⁻² ?
 A: You experience a backward force when you hit the brakes, and so yes, you are accelerating backwards.
Acceleration is a physical concept that is a vector. It also happens to be a word in English which loosely means ''to speed up''. Deceleration is an English word which is the opposite of acceleration in that sense. But that's clearly not the same as tacking on a minus sign. 
I disagree with the earlier answer that says that deceleration is just the negative of acceleration. Indeed, a common problem arises for students who -- when they are dealing with a freely falling object -- find that if they choose the conventional coordinate system, the acceleration is $-g$, but the ball isn't ''decelerating'' since it is clearly speeding up as it falls. The negative sign here just means the direction is along the negative $y$ axis, and just indicates the direction in which the velocity is changing. 
If I had to define it in physical terms, I would say that deceleration occurs when the velocity of the object (a vector) and the acceleration of the object (another vector) are in opposite directions. In other words, it tends to bring the magnitude of the velocity to zero. This is what happens when you step on the brakes of a moving car.
If you're still unsure, consider the following questions:


*

*Can you accelerate a body in motion?

*Can you accelerate a body at rest?


Now ask yourself the following questions:


*

*Can you decelerate a body in motion?

*Can you decelerate a body at rest?


You should see that the concept of deceleration requires an object to possess a velocity for the question to make any sense.
A: 
I am slowing down (decelerating) am I then accelerating backwards?  

The implication here is that the direction of the acceleration is in the opposite direction to the velocity.
I think that you should avoid the word decelerate as it can be taken to mean a reduction in the speed of the car but this might not always be so.  
Suppose a car is moving at $\rm 10 \, m\,s^{-1}$ up a hill and suddenly the engine stops working and the brakes are not applied.  
The car then decelerates down the hill at $\rm 2 \,m\,s^{-2}$ ie it has an acceleration of $\rm -2 \,m\,s^{-2}$ up the hill.
So after $1\,\rm s$ the velocity of the car is $\rm 8 \, m\,s^{-1}$ up the hill and after $5\,\rm s$ the car is at rest.
All fine so far as the speed of the car has decreased from  $\rm 10 \, m\,s^{-1}$ to be at rest.  
However what happens after $6\, \rm s$?
The velocity of the car is $\rm 2 \, m\,s^{-1}$ down the hill ie the speed of the car is now increasing.  

If I am decelerating in this car at -5ms⁻² am I accelerating backwards at 5ms⁻² ?  

Let the car be moving in the positive x-direction.
A deceleration implies that the acceleration is in the negative x-direction.
A negative deceleration implies that the acceleration is in the positive x-direction.  
With the car moving in the positive x-direction a deceleration of 5ms⁻² implies that the car has an acceleration of 5ms⁻² in the negative x-direction.  
With the car moving in the positive x-direction, a deceleration of -5ms⁻² implies that the car has an acceleration of +5ms⁻² in the positive x-direction.  
