Given an opamp to which we can apply a supply voltage of 5v. Does this mean it has to be only +2.5 and -2.5 V or could it be 0 and +5v. Is there a difference?
Thus is it possible to convert any opamp to a single supply opamp
Any opamp can be operated from a single supply, as long as the circuit is arranged properly.
Some amplifiers are advertised as 'single rail', when they have an input common mode range and an output swing that includes the negative rail. This feature often simplifies the circuit when using the negative rail as ground.
Some circuits lend themselves more easily to being referred to a 'ground' at mid supply, or the negative supply, or a less well-defined level between the rails.
Generally if an opamp just has a V+ and a V- pin with no separate GND pin then you can operate them with either a unipolar supply or a bipolar supply.
The important thing to keep in mind is that for a unipolar supply the virtual ground of the opamp is going to be half the V+ supply voltage. So in the case of the 0 to 5V operation you asked about the virtual ground will be at +2.5V.