Q: Understanding Processor specifications I'm not sure what a CPU-specification like "3 GHz Intel Core i5" really means.
Does it mean that there are five cores with 3 GHz each? Or are there 3 GHz distributed between the five cores?
What would be the equivalent, if it would have only one single core?
I mean: One can not say, that it is equal a single core with fifteen GHz, I guess ...

A: Side note, Intel's i3, i5, i7, and i9 naming schemes don't tell how many cores there are (they used to, I believe, but they weren't 3, 5, or 7). Cores are also almost always distributed in even numbers.

3 GHz

This means the speed at which the processor runs at. GHz is Gigahertz, or billions of hertz. Hertz is basically the number of times per second something is run. A 60Hz monitor refreshes its screen 60 times per second. In the case of CPUs, GHz is in reference to the number of clock cycles, which can contain one or more instructions per cycle. This also means that comparing GHz is a bad idea, as with each new generation of CPUs, clock cycles are used more efficiently, and in different ways (between Intel and AMD and especially ARM-based processors)

Intel Core i5

The CPU is made from Intel, it's part of the "Core" lineup, more specifically the i5 lineup. i[number] used to mean it had a certain number of cores, whether it had hyperthreading, and I think few other things. It no longer means that. An i5 can have 2 cores with hyperthreading or 6 cores without, and anywhere in between. Without more info, such as the model number (i5-2500, for example), not much else is known about the CPU. With the model number, you can look up various information about the CPU. This includes information such as the number of cores it has, which means how many individual threads can be run at once.
Even comparing two CPUs with the same GHz, core count, and generation doesn't mean they're identical. There are different processors for mobile, desktop, high end desktop, etc. A 3.0GHz 4 core laptop CPU runs with significantly less power and heat (and thus has less computing power) than it's desktop counterpart
To answer your final question, no, you cannot multiply GHz by cores. If we assume two CPUs are identical in every aspect except for core count, say a 3.0GHz 4-core and a 3.0GHz 8-core, we can't say that the 8-core is twice as powerful. Let's say you have a factory, which produces blankets. Each blanket takes 3 hours to sew. With 4 workers, you can produce 4 blankets every 3 hours. With 8 workers, you can produce 8 blankets every 3 hours. However, even if you have 100 workers, you still can't produce a blanket in less than 3 hours, since that's the time it takes to produce a blanket. This holds true for CPUs. Depending on what you're doing, you may not get any benefit from multiple cores. Some tasks can be heavily multithreaded. In our example, this would mean each part of the blanket could be made different people, then stitched together at the end. Other tasks cannot, such as growing a crop. You can have 10,000 crop fields, but you won't be able to harvest any faster than if you only had 1 crop. 
