The short answer: Find the color in your Color Bridge Guide,
set up the corresponding spot color in Illustrator 2017 CC and use it. Without the Color Bridge Guide or a Solid Color Guide, the Pantone Connect Service is the only other official way, to find a matching Solid Pantone Color on the basis of CMYK values. There are private sites offering some conversions, but in my experience, they're not the same to official values.
TL;DR; The long answer:
Some days ago unfortunately Pantone closed its free Color Finder site, where you could compare and convert every Pantone color. You could have typed your CMYK values and would have gotten a bunch of suggestions for fitting Pantone Solid colors. That would have been my first choice. The similar, but new Pantone Connect Service isn't free for conversion feature and I didn't use it so far.
That forces me to have a look on the Color Bridge Guide or into the Pantone Color Manager, where I need to find the closest matching CMYK value by more or less trial and error. First, I'd choose a look into the Guide.
In case of your sample CMYK value 15 0 71 0, it's a little silly as Pantone seems to have an error in its system, at least on my Pantone+ Guide. In the Guide, the value doesn't exist and I'd need to choose a close match like 15 0 80 0 (Pantone 388 CP) or 14 0 68 0 (Pantone 585 CP) -> a good close match. CP stands for coated (paper) and process (colors). In my Color Bridge Guide the number 2296 CP does probably have got wrong values 17 0 54 0. In contradiction to this, the Pantone Color Manager tells me 15 0 71 0 for 2296 CP, like the values of your sample image. It can be, that there was an update or simply a bug. I'd have to call Pantone for support and further explanation.
Besides that abnormality, let's say 2296 CP is printed with 15 0 71 0 and I'd like to print the genuine Pantone color instead of the process color, I'd simply need to set up a new color in Illustrator (version is irrelevant), choose spot instead of process, name it "PANTONE 2296 C". Just for convenience, I could choose to display the colors with the corresponding values 15 0 71 0 or with 100% key color 0 0 0 100 or any other color value, as it's just for the visualization on the display to make it look right. Even the name of the spot color is not fixed. You could also choose to name it "PMS 2296 C" (
Pantone
Matching
System) or write it in small letters. It doesn't matter, as long as your printer chooses the right color. As there is no complete automated process for ordering the color or mixing it and fill the special color in the offset printing machine, a human being needs to understand what you want and execute it. In the Solid Guide, there is the recipe for mixing the color. For "PMS 2296 C" it would be PANTONE Green 1,54%, Pantone Trans White 89,76%, Pantone Yellow 012 8,70%. The printer can order the already mixed color "PMS 2296 C" or can mix it by himself. The result of the recipe may vary, as some more or less ingredients changes the whole mixture a bit. If the color is filled into the printing machine, the printer can choose different amount of pressure over the whole size of the sheet of paper. That makes the color appear more or less dark. To get a close matching "PMS 2296 C" in the Guide, it needs a lot of prints and a lot of experience of the printer and not to forget, motivation to control the exact matching, instead of just being lazy and not moving the knobs. So far so good? No, the printer has another reference Guide and different measuring tools, compared to you or another printer. As a result, even Pantone colors are varying a lot. Is it worth using them? Yes, I think, it is worth using them, but the costs are often too high for an average client.
Think more of a definition, than of a color. What is important to know is, that a spot color is always on a separate color channel. If you print CMYK + "Pantone 2296 C" you'd get 5 formes or plates. The 5th plate will print your extra (spot) color. Again, if you only consider the plate, it doesn't matter which color will be printed it's just a monochrome rasterized image that can have more or less density parts to give you no 5th color or any coverage until a full coverage. And it mixes up with your other 4 colors, if it's printed one over another.
To get back to Illustrator. Just define the color, name it so that a human being understands you, what color you need, apply it on your graphics, create a PDF with the color profile that fits your paper and printer recommendation. Finally control, what's inside your color channels in Acrobat Pro's Print Tool for Separation. There you'll see all of your color channels and you can move the cursor over any color, to see with how many percentage from 0 to 100% each part of the design is covered. Then there is a value for colors in total that sums up every color. It mainly depends on your paper, how much coverage is valid. Some printers don't allow more than 300% in total. A maximum should be 320% to 330% for
coated paper (the
C in the color name).
If you've got further questions, please give as much details as possible where exactly you're struggling.