I'm not pretty good when doing aural analysis, but I can't seem to get the hang of time signature. My teacher said 4/4 is the most common time signature, and I could take a big gamble in writing 4/4 each time, but no. I want to understand how to identify a song ad 3/4. 5/4/ so on. But it always comes back to 4/4, they all sound like 4/4 almost. I've tried watching videos, but I can't seem to understand.
First of all, don't listen to songs by watching videos: your mind is concentrating more on the pictures than the sound. Close your eyes and listen!
Secondly, you need to train your ears (and body) to distinguish between 4/4 and other time signatures, especially 3/4 and 5/4. It would be best to listen to unambiguous examples of songs in these time signatures then compare them to "other songs". I'm a child of the '60s so my examples are very old!
Waltzes are in 3/4 time. Most music with the name "waltz" in its title will be in 3/4 although this is not necessarily foolproof. "She's leaving home" and "Norwegian Wood" by The Beatles are in 3/4 time. "Gymnopedie #1" by Eric Satie is in 3/4.
Two iconic songs in 5/4 are "Take five" by Dave Brubeck and "Living in the past" by Jethro Tull. There are many discussions about 5/4 time here; many consider that a bar of 5/4 can be subdivided into a bar of 3/4 and one of 2/4. A classical piece in 5/4 is "Mars" from the Planets suite by Gustav Holtz.
Probably the best known song in 7/4 is "Money" by Pink Floyd, although I am told that the guitar solo in the middle is played in 4/4.
The answers already here are great. Forgive me if this is covering something you're already on top of, but let me take it back to the very first step.
So time signature ("meter") is all about how beats are grouped together. That assumes that there are beats. Listen to this:
This shakuhachi performance is "unpulsed"—it doesn't organize itself around beats. It has long and short notes, but they don't come at regular intervals. Compare to this:For the first 15 seconds we're not sure where the "beat" is, but as soon as those bass notes come in there's no doubt. Each piano note with bass drum kick is louder than the milliseconds between them—it's an emphasis—and is spaced evenly. This music is hella pulsed.
Okay, the next question becomes how these beats fall into groups. Continuing to listen to the "Gentle Rain" remix, after the first 8 introductory beats, the full drum kit gets involved* and the piano does a little pattern. But the piano still marks certain beats with a loud bass note, and the drum reinforces it with a bass kick. At this point, stop analyzing, and just stand up and bounce to the beat. (If you feel silly, you can use a fancy word and say you're practicing eurhythmics.) You'll probably find yourself moving a certain way on each beat, and probably responding to some beats more than others. Feel the "weightiness" of those bass-piano-and-drum notes, and start to notice how many beats separate them: they come along every four. This is the "downbeat," the first and strongest beat of each measure. The "gravitational" pull of this beat is like the sun in the solar system, and the rest of the beats just move in its influence. A piece of music can choose to temporarily de-emphasize a downbeat, but the idea of it is still there, or else we'd wind up hearing a different beat as the start of the group. (Perhaps this song was a bad example to choose, since there's a strong snare crack on beats 2 and 4, the "weak beats" or "off beats". The idea of emphasizing the "offbeat" is central to many musics from 20s jazz to power rock, but they're still the offbeats because there's an understanding that beat 1 is where it all starts. If the offbeats were actually the strong beats, we wouldn't get such a subversive thrill from emphasizing them. (In this track, those bass notes mark it out in black and white. It's only a rule of thumb, and isn't true 100%, but you can often find the beat by focusing on the bass.)
Now, you threw yourself a curve ball by mentioning 5/4. There isn't a lot of music with 5 beats. But listen to perhaps the best-known example:For the first few seconds we just have a lot of drum noise. But again, focus on the bass drum: it just drops a single kick every so often. The syncopation in the cymbals might make it hard to count, but listen to the piano as it comes in. It plays a short series of notes and repeats it several times. This repetition can also help you find where each measure starts, as it lines up with those bass kicks on the downbeat. Try to count between each downbeat, and remember that beats are all the same distance apart (see footnote below), so don't get tricked into counting in long-and-short numbers along with the rhythm that they're playing. If you get the hang of it, you'll find you're counting to five before starting over each time.
* I almost wrote, "at this point the beat comes in." This points to an important distinction between two ways the word "beat" is used. We often use the word "beat" to mean "a certain pattern of long and short notes," as in "Jay-Z laid down a beat for my new song" (I can dream!) or "that song has a samba beat." But in your question and these answers, and in a music theory class, the "beat" doesn't have to be the notes you hear; it's an idea lying under them. For an analogy: if you draw a picture on graph paper, the lines of the graph paper are "the beat." They're spaced evenly apart and lie under the picture; you then make shapes on top of them, moving through and around them. For this formal, music-theory set of definitions, those shapes are "rhythm." A rhythm can be made up of notes of different lengths, but every beat is always the same length.**
** Well, until you start warping time with slow-downs, speed-ups, pauses, and so on, but—well, you could curve the graph paper and the lines would still be there. You might not even know it's curved without the lines.
The majority of most types of music puts extra emphasis on beat 1. Knowing where beat 1 is will make the job easier. So listen to uncomplicated pop songs, and sing songs that you already know.
Tap just on the most emphasised note each time it occurs. That will be your 1. In songs, there is often an important word for that beat 1. Then tap along with the rhythm of the song - with steady, regular taps in time. Make your 1 louder, to match the music. When you're happy that you match what's played, count the 1s, and count up for the remaining beats, reverting to 1 every time it's emphasised. The highet number you reach regularly is the number of beats per bar - the top number in the time signature.
Be aware that the 1st note in a song won't necessarily be beat 1 - there's sometimes an anacrucis.
Answering 4/4 will probably get it right 60-70% of the time, but good on you for wanting to get 100%! I just wonder what your teacher is doing about your problem, though...