This is my first time using InDesign to make something and I have never had an issue like this.
Stands to reason that you never had an issue like that.
Exporting to PDF requires you to choose an output profile. The "High Quality" PDF export is only a starting point. When you export a PDF you can choose to have "No colour conversion" which will give you the same values as your inDesign file.
But you should probably choose an output profile that matches your printer.
If you output to a specific output profile then the colours will Change. You can avoid this by choosing "Convert to Destination (Preserve Numbers).
This is all available in the File>Export>PDF (Print) and in the Output section of the dialog box.
And to add to that - if you think that you'll get this colour printed by a professional printers to match, then you need to send them a sample of the colour you are looking for that is printed from you and ask them to match that.
The fact is that most pure blue colors are out of gamut for CMYK printers. In other words, the color cannot be accurately reproduced. The same is true for many RGB colors such a pure bright green. To check these prior to attempting to print or create PDF for a workflow that requires CMYK printing, use the View=>Proof Colors function. You'll see a rendition of what your content will look like in the destination CMYK color space. Note that this doesn't mean you export RGB as CMYK, but rather this is what will render when printed or on screen if there is transparency blending going on.
As Dov states, many colours that appear nice and bright on your screen won't be reproducible when printed CMYK, which has a much smaller range of colours (gamut). The process of trying to cope with these issues is known as colour management and it might be worth you learning more about this, including how to calibrate your monitor, using profiles, and using soft proofing.
I've just noticed that this tutorial on Color Management is available on special offer of $32.99 instead of $59.99: Color Management for Photographers and Designers: Learn by Video | Peachpit Available as a DVD or as an Online Video.
(I have no connection with Peachpit)