Fret Markers

What is the significance of having fret markers at 5,7, and 10? How about that placement of the others farther down the neck, if a uke has them?

I'm assuming you are asking what is the origin/history of fret markers? I got curious and found this on Wikipedia. As I would have guessed, it comes from guitar:

On guitars, there are two popular fretboard inlay schemes:

• The most popular (1) involves single inlays on the 3rd, 5th, 7th, 9th, double inlays on the 12th, single inlays on the 15th, 17th, 19th, and 21st, and if present, double inlays on the 24th. Advantages of such scheme include its symmetry about the 12th fret and symmetry of every half (0-12 and 12-24) about the 7th and 19th frets. However, playing these frets, for example, on the E string would yield the notes E, G, A, B, C# that barely make a complete musical mode by themselves.
• Resonator Guitars usually have inlays like the first scheme shown above but with a single inlay on the 12th, and double inlays on the 15th.
• A less popular scheme (2) involves inlays on 3rd, 5th, 7th, 10th, 12th, 15th, 17th, 19th, 22nd and 24th frets. Playing these frets on the E string yields the notes E, G, A, B, D that fit perfectly into the E minor pentatonic scale. Such a scheme is very close to the coloring of a piano's keys and is of some use on classical guitars.
• Some guitars like the Gibson Les Paul Custom will also have a single inlay on the 1st fret, then follow one of the above schemes.

With ukes though, I've found a lot less consistency. I've had some that only had them at 5, 7 and 10; some that had them at 3, 5, 7, 10 and 12; some that had side dots as well and some that just had fretboard dots. I never use the side dots, but that uke that didn't have them at 12 really scrambled my brain - so much that I added a white paper sticker on 12!

The 5th and 7th fret show the fourth and fifth interval, and the twelfth fret is the octave. the 9/10th fret... I dunno.

I don't know what they signify ...but I sure as hell am grateful cos' I use them like road signs or ready reckoners ....saves having to count frets...and harmonics come into to it somewhere as well....you can get harmonics easy on the twelfth but also on the fifth and seventh ...just take's a little more finger release /pinch synchro
thingy.....co-ordination.....

CeeJay

Most of the fret markers denote harmonic points. This is particularly true of 12, 7 and 5. I think 3 is perhaps a less easy harmonic. Beyond that you are splitting hairs.

I've had ukes with just one side marker at 7 using the body joint at the 12th as the far 'maker'. It worked fine.

While I only need one landmark in the fretboard, I do prefer the full complement at 3, 5, 7, 10, 12 and 15.

I've got a Favilla baritone which was made with guitars in mind and has markers at 5,7,9,12, and 15.
Not sure why guitars mark 9 and ukes mark 10. Always throws me off.