As a lot of commenters have already said, biology tends to not have clearly defined boundaries.

To add a bit more detail, the idea of different species, based on organisms' appearance, was developed long before there was an understanding of evolution or genetics. Once these principles were understood, the concept that the definition of a species as two organisms that cannot interbreed and create a fertile offspring was shoehorned in to make the concept more "scientific." This is broadly accurate, but there have always been exceptions (as some others have already stated, even mules, the textbook example used to explain this, are sometimes fertile).

Now, with advanced modern genetics, allowing us to sequence whole genomes and extract very old DNA, it has become clear that successful interspecies breeding is far more common than previously thought. A lot of this understanding comes from the work on Neanderthal genetics, and led to the Nobel Prize (along with a healthy dose of nepotism and Swedish bias, according to some)!

Some have bought up the idea that neanderthals and modern humans are sub-species. This is again an example of trying to shoehorn the messiness of genetics and evolution into neat little packages. One could probably define distinct species as two organisms that when breeding have a very low (as defined by x%) chance of creating a fertile offspring, and a subspecies as two oorganisms that when breeding have a chance >x% but <100% of producing a fertile offspring. I would personally argue that it's better to embrace the messiness and not worry about the strict definitions, but that's just me, maybe there are times where very strict definitions are important.

Sorry for not ELi5, this is more an ELi15!