I was watching

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His circuit diagram in the beginning of the video suggests that he will be using 5uf capacitors. Later in the video he appears to use two 10uF electrolytic capacitors by connecting their negative sides together.

Is this common usage? Will it damage the caps, or is it ok?

 

If not using the Neg connection for any other but only both +ve's, then it becomes a bi-polar (series) capacitor at half the capacity.
Max.

 

Elliot Sound Products ( http://sound.whsites.net/lr-passive.htm ) says that electrolytic capacitors in a passive crossover network are inappropriate and that an iron core in an inductor also causes audible distortion then inductors are almost always air-core. He says that an active crossover is much better than a passive one because the speakers heat up which changes their impedance.
None of my home-made or purchased speakers use electrolytic capacitors or iron-core inductors then they have very low distortion.

 

Using back-to-back polarized capacitors is a sort of effective method of achieving a non-polarized capacitance value. As for distortion, that depends on a lot of things, including the leakage current of those 2 capacitors. Will they work ?Yes. Will they be every bit as good as a non-polarized capacitor would be? Not quite. Will the distortion be enough so that you can hear it? That is a much harder question.
using the two capacitors has been done for over 50 years, and a lot of folks think it is just fine. Others claim that it sounds bad. Of course,
There are folks who claim to be able to hear levels of distortion far lower than what can be measured with the very best equipment. They claim to be able to hear the difference between their $250 speaker cables and an equal sized equal length piece of ordinary electrical wire.
Those folks can easily spot a distortion level of 0.0001%, far below what most top grade equipment can detect.
So the final answer is "Does it sound good to you?" What others think does not really matter in this case.

 

Electrolytic coupling capacitors and iron core inductors are measured to cause distortion which muddies the sounds. Why save the cost of only one cup of coffee instead of using high quality low distortion film capacitors and air core inductors?

Lots of old/deaf people cannot hear high frequency audio distortion that is heard by everybody else. They like the sound of an awful muffled old AM radio.

 

Is this common usage? Will it damage the caps, or is it ok?

This is also basically how a AC induction motor start capacitor is constructed, operating on AC it has to conduct a very high current for a very limited time.
Max.

 

There are folks who claim to be able to hear levels of distortion far lower than what can be measured with the very best equipment. They claim to be able to hear the difference between their $250 speaker cables and an equal sized equal length piece of ordinary electrical wire.
Those folks can easily spot a distortion level of 0.0001%, far below what most top grade equipment can detect.
So the final answer is "Does it sound good to you?" What others think does not really matter in this case.

In any case, at reasonable and appropriate sound levels using the two caps back to back will not damage them. That is, the voltage rating of the capacitors should be appropriate for the voltage applied. So if your amplifier is putting out 150 volts across the 8 ohm output, you should be using 150 volt capacitors. But most folks do not use nearly that much power.