If it says to use 10-10-10 on a plant.
What is the difference between 10-10-10- and 5-5-5 fertilizer?
Just use twice as much 5-5-5 or half as much of 10-10-10?

The RATIO of both products is 1:1:1. The NPK numbers on the label are the PERCENTAGE by volume in the package in (various fillers and/or other nutrients make up the remaining percentage). It's always best to follow the manufacturer's application instructions, but essentially yes, the lower percentage will require a greater volume of product to achieve whatever application strength you're aiming for.

Whether your plants actually need that ratio is another subject. This guy is annoying to listen to, but his message is valuable.
https://youtu.be/1COpSNWSG8o?s...

But anybody who is recommending a "balanced" fertilizer (where the numbers are the same) probably doesn't know much about plant nutrition or soils.

If you watched the link @lochroma, you'll see that issue is fully addressed.

Whatever. I'm not watching that video. I had 4 years of Horticulture including a year of soil science.
To the OP: If you're going to buy a fertilizer like that you might as well buy 20-20-20 as it's more bang for your buck. You could dilute to the proper concentration.

I watched it and also read the comments. He has an interesting take but may have gone a wee bit overboard in his conclusions. And a lot of his viewers don't agree (but at least they watched before deciding he was full of .... ). I want to see his credentials but can't even find his name.

Lucy, I agree. I often find him heavy-handed and overly opinionated, but often there are thruths as the basis of his wordy lectures. I listen to him at 1.75 speed.

There are other horticulture figures out there who also started out extremely knowledgeable in their given niches but got popular and turned into overbearing "experts" about all things garden-related. I believe in science, but also believe there is usually a little wiggle room when it comes to most gardening practices.

If 1 bought 20-20-20
What do I reduce it with or just use 1/4 the amount to make 5-5-5?

If you use less it'll just be weaker. Those numbers represent the volume of the named elements (NPK) in the package; the lower the volume, the more filler. (Note, I've clarified this in the following post below.)

However, both products hold the same ratio of those ingredients to each other: 1:1:1.

Understand this>>> the application instructions will account for the concentration. The 20 might say to apply, say, a quarter of a cup per plant and the 5 might say to apply one cup and both will deliver the same amount of NPK in the same ratio. If you want to use less fertilizer for a weaker application, sure, use less, but the ratio remains the same.

I'm answering only your direct question (rather confusedly I fear) but I'll briefly address the need for them. There is an abundance of scientific literature that contends that ratio contains an overload of phosphorus, which has been determined unnecessary in most home gardens. Many authorities now recommend ratios in the neighborhood of 3:1:2, but everything depends on your soil, and what you're growing. Have you had your soil tested to determine that you need that much?

To add and clarify, should've phrased the first paragraph differently: it's volume by percentage. NPK 20-20-20 means that the product in the package is composed of 20% nitrogen, 20% phosphorus, 20% potassium. The remaining 40% can be many different things like other beneficial nutrients or inert spreading materials.

But as mentioned, however much you apply, the 1:1:1 ratio among those primary nutrients doesn't change.

Apologies if you already know this. I felt I was unclear about what those numbers represent in case you didn't know.

Another edit: I only just realized this is a continuation of an existing thread. The preceding discussion didn't show on my phone screen and I thought it was a new question. Doh!!
Maybe it would help if you tell us what you're trying to achieve. The important thing is to follow the instructions on the package.

@Lee242 - what sort of plant/plants are you using the fertilizer for?