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You've got the right idea. Partly.

An LED used with a series resistor does waste the energy dissipated in the resistor. Depending on the voltage from the power supply, you can easily waste more energy in the resistor than you use for the LED.

So far, you are correct.

What I want to correct is the idea that the resistor is there to lower the voltage.

The resistor is there to limit the current.

LEDs are current driven devices. The forward voltage varies with current and temperature.

To get a stable brightness out of an LED, you regulate the current.

You will have noticed that the calculation for the series resistor uses the desired LED current. You take the difference of the supply voltage and the (approximate) forward voltage of the LED, and divide that by the current to find the value for the series resistor.

If you tried to regulate an LED only by regulating the voltage, then you would destroy your LED very quickly. Just below the forward voltage, the LED doesn't light up at all. Just above the forward voltage the LED becomes the next best thing to a short circuit. There is a tiny range in between where it lights up and passes only a little bit of current.

That little range is impossible to hit with just a voltage regulator - it moves with temperature and current - current makes the LED get warmer, and warmer makes the LED conduct more. You would be varying the voltage up and down wildly with some kind of feedback circuit measuring the current.

Or, just regulate the current to begin with. Provide no more current than needed to light your LED at the desired brightness, and let the voltage do as it pleases - the voltage is of no interest.

No, you are not missing anything. The energy consumed by the resistor is wasted but, if you were contemplating a circuit that used tens or hundreds of LEDs you might consider a buck regulator to step the LED circuit supply voltage down to maybe 3 volts and make a significant net power saving per LED drive.

You’ll still need a 50 ohm resistor but it will only be dropping around 1 volt and dissipating only 20 mW.

The good news is that many modern LEDs need only a couple of mA to obtain sufficient brightness for “standard” applications.

One point I would like to mention is the circuits which are meant to be drive LEDs. The constant current circuitry can come in handy to save power when multiple LEDs are needed to be driven.

In general it is desired to drive the LEDs with a voltage just close to the forward vorlage drop. The voltage is only needed to bias the LED. The brightness should be controlled by the current through it. A BJT and opamp can act as a simple constant current circuit. The issue is critical when driving LEDs in series or high power LEDs.

Depending on the number of LEDs and the cost or power criteria decision should be made. Leave it as is with the resistor combination. If the power saving is a must, rethink about the whole strategy of supply voltage levels and LED options. Other answers have put light already on low power options

Here's what you're missing. Your power supply has a given potential: 5 V. That isn't going away. When you put 5 V across a component that can't handle it, you must do something with that extra potential or you will unbalance the voltage/current ratio in the circuit-- and the component will be damaged (in this case the LED).

The LED is not in and of itself strong enough to resist the potential applied across it - that is specifically why the datasheet is telling you it can only withstand a potential across it of 2 VDC. That's the first thing. The second thing is how much current you blow through it - in this case, the datasheet apparently says 20 mA. Understand that just because a datasheet provides a maximum current value of 20 mA, it does not mean you should actually operate the device at that level (or should you). There will usually be no appreciable difference between 8-10 mA and 20 mA, depending on color.

The resistor you use is doing a couple of things - it is taking up the slack for the voltage the LED can't handle, and it is limiting the current through the LED to what you designate you want to run through it.

The heat being dissipated by the resistor is not excess or left-over; it's actually only the heat being generated by the amount of current you are limiting the LED to. That's an important point. The resistor cannot dissipate energy that isn't flowing through it. And it certainly is not carrying the full current of your power supply.

So, Ohm's law says:

R = E / I
R = (5 V - 2 V) / 0.008 A
R = 3 V / 0.008 A
R = 375 ohms

In this case, we'll go with 360 ohms (it's the closest available).

I = E / R
I = (5 V - 2 V) / 360 Ω
I = 3 V / 360 Ω
I = 0.0083 A (or 8.3 mA).

Now that you know how much current is flowing, and what resistor to use, you can calculate how fat a resistor you need, based on what it's dissipating:

Watt's law is handy here:

P = I * E
P = 0.0083 A * 3 V
P = 0.0249 watts
P = 24.9 mW

Now that you know how much energy is dissipated, you can size the resistor. An 8th watt (1/8th of a watt) resistor will dissipate 125mW. For safety, you want a resistor that can handle twice what your power requirements are. Therefore, 2 * 24.9 mW = 49.8 mW. That small amount is far less than 125mW, so you can use an 8th-watt resistor.

I hope that helps.

LEDs are designed to be driven at a particular current.

The ideal way to drive them is with a current source, such as a switching power supply operating in constant-current mode. This will be the most efficient usually, but on very small loads like this, its overhead may be worse than the resistor.

The resistor is basically a super cheap way to convert a constant-voltage source into a current source (I didn't say constant). Like any resistive regulator (think LM7805), it wastes a lot of energy as heat.