Adding to Passerby's answer: Replicate what's on the strip. It wastes the least current. The strip is made up of repeating circuits as shown below.
simulate this circuit – Schematic created using CircuitLab
You should do the same. Polarity of LEDs matters. The resistors can go anywhere in the series circuit - they're probably evenly spaced on the strip to spread the heat.
You haven't provided much info. First white thing is labelled as transformer for "LV Halogen Lamps". Most likely it's just a step down transformer which will fry your christmas LED strip during reverse polarity.
Second one is a mystery box without much info. I wouldn't go for that either.
Here is what you need to do:
Figure out what voltage is required by your LED strip - 3V, 5V, 12V or something else?
If the LED strip is 5 watts, then you can calculate the current requirement as follows:
Current = Power / Voltage required.
Ex- If LED strip needs 5V, then you will need 5W/5V = 1A of current.
Go to the market and ask for a 5V 1A(or higher) wall adapter. Modify the voltage and current accordingly. I am just giving an example.
Get something less intimidating like this:
EDIT after the question was edited:
Figure out what length of strip you want to use. I will assume 0.7 meters which will give you total power requirement:
Power = Length X Power required per unit length = 0.7 X 7.2 = 5 watts.
Voltage = 12 V
Current = Power / Voltage = 5/12 = 0.42 A
Better to go for 12V 0.5A (or higher) wall adapter or any DC power source. Make sure it's a DC power source and not just a step down transformer. If the power source is DC 12V 12W, then it will do the job without any issues.
Best Answer
I trust the meter, and I assume the power supply is a 'wall-wart' style encapsulated blob which provides a few tens of watts at most. (A picture would certainly help.)
Also, since you didn't specify conditions, I assume you measured the output of the power supply with no load.
My guess is that it's a loosely-regulated one which drifts high as the load decreases. Read the label and apply the rated load (i.e. if it's 12V / 2A - apply a 2A load) and see what the output voltage is.
The suitability of this power supply for your LED strip is going to depend on a number of things, including how much current the strip is going to need. If the supply is rated higher than what the strip needs, the voltage will likely be higher than 12V and you may get more current than you bargained for (brighter LEDs maybe).