Obviously running your engine at too high an RPM for too long isn't good. But what about running it too low? not so low that it stalls or lugs, but within around 1,000 RPM?
Would you get better gas mileage? Would it wear out the engine or transmission faster?
For example, going 20 mph in 5th gear down a quiet city street that you know has no stop signs for half a mile or more.
To answer your question, no it isn't bad for your car to keep it in as high a gear as you can while still maintaining speed. As long as you are above idle in RPM and your engine isn't lugging, you aren't doing any damage.
See this link for more information about lugging.
You mentioned that you might do this to be quieter and for fuel efficiency. Your car will certainly be quieter, so this is one advantage. As for fuel efficiency, there is such a thing as being in too high a gear in certain situations. Because of the vacuum created when the throttle is closed, and it will be close to closed at such a low RPM, you could potentially be making your engine work more to maintain speed than you would be if you were in a lower gear. This would mean you wouldn't be driving at optimum fuel efficiency. Of course, this depends on your car and many other factors, so there's no way to be sure being in 5th gear is worse for your fuel economy than being in 4th gear at such a low speed. If I had to guess, you will still be getting better fuel economy in 5th gear at 1,000 RPM.
When in doubt, to maximize fuel efficiency, use as high a gear as you can manage for the power required.
tl dr - Yes to mileage; no to wear.
Would you get better gas mileage?
The general rule of thumb would be to run your vehicle in the highest gear possible without lugging the engine. This means if you can drive down the road at 1000rpm at 20mph, you will get better gas mileage than you will driving 20mph at 1500rpm. When you try to accelerate in the higher gear, this is where you will experience higher fuel consumption because you will need to be on the accelerator longer in order to obtain the higher speed. This is due to the lower torque available to the rear wheels. In a lower gear, relative torque is increased and you will gain your higher speed faster with the same (or less) amount of throttle input, which means you can upshift your transmission and get your RPMs down again.
Would it wear out the engine or transmission faster?
Just cruising at the lower speed in the higher gear will not incur any extra wear to engine or transmission. In fact, you'll see less wear due to running the engine at a lower speed. That difference will not be much of a difference, but there will be a difference.
If an engine is ran within tolerance (normal driving) for it's entire life, maintenance is kept up, and all else is normal, it stands to reason that there will only be so many revolutions an engine will make until it is worn out. If there is a set amount of revolutions an engine will make, running it at a lower rpm at the same vehicle speed will help it to last longer.
To reiterate something, though ... all that I wrote is dependent upon your premise of a flat road without stopping or accelerating. When you throw any hills, slowing, or speeding up into the mix, all bets are off. Downshift as needed so you aren't putting undue strain on your drive train.
The answer depends on the size of car and type of engine, but a modern car might have the tools to answer the question built-in. On my (base model, small, European, 6-year-old) car, just switch the dashboard display to show instantaneous fuel consumption and drive at constant speed on a quiet road. The current base-model version of the same car also comes with a gear-change indicator that suggests when changing up a gear will save fuel. I've only driven that model a few times, but it certainly suggested 5th gear instead of 4th at below 30 MPH in town driving. That gave about 1000-1200 RPM compared with the hot idle speed of about 850. (The logic includes the throttle position as well as the RPM - i.e. if you are trying to accelerate in the current gear, it is less likely to suggest you change up.)
Unless you try something unrealistic (like trying to drive up a 20% gradient in 5th gear at 30 mph) the engine management system stops RPM dropping below idle speed in any case, by increasing the fuel supply.
In the last ~10 years, new engines have been designed to allow you to run them at lower rpm without lugging or hiccuping. The Volkswagen-Audi TFSI engines, for example, are built to run well at 1000 rpm in top gear. Older petrol engines I've driven needed closer to 1500 rpm to run smoothly.
This probably depends on what kind of engine you have, but engines having variable valve timing (VVT) technology can perfectly well run at very low RPMs. For example, I used to have a 2011 Toyota Yaris with 1.33 litre engine having VVT on both the intake and the exhaust. The engine could perfectly well propel the car at constant speed at idling RPMs on level ground if a low gear was selected. The idling RPMs vary from 500 RPM to 1000 RPM depending on the conditions.
For Toyota's simulated Atkinson cycle hybrid engines (that have VVT only on the intake), we know the engine operating lines which are computer-optimized to optimize fuel economy. The old 1.5 litre 1NZ-FXE had the operating line start from 1200 RPM and the new 1.8 litre 2ZR-FXE has the operating line start from 1000 RPM. For the bigger 2.5 litre 2AR-FXE engine the operating line is unknown, but presumably it is similar to the 2ZR-FXE. The hybrid vehicles using these engines (Prius etc.) run the engine most of the time at the lowest possible RPM. This is possible given that you don't demand too much torque from the engine at such low RPMs.
So, I would say that if your gas pedal is not more than halfway to the floor, you can perfectly well expect modern VVT engines to produce power at 1000 RPM, given that Toyota's hybrid eCVT runs the engine most of the time at this RPM. This applies even to engines having VVT only on the intake. However, please do keep in mind that if your power demands increase due to needing to accelerate, downshifting is advised. If driving a manual transmission car, double-declutch when downshifting!
