How can I get 15 HPS score?

Are you sure that the keyboard you're using is physically capable of that many presses per second? It might take longer than that for the spring to snap the key back into place. Sort of like how upright pianos can actually make some pieces very hard to play (can't hit repeated notes at-tempo because the hammer needs more time to retract) because of physics. You might need a quality mechanical keyboard optimized for it.

It's also fairly trivial to program sending keyboard events to your browser, so really you could quite easily reach whatever number of 'HPS', or however fast that site can count it. It's pretty much impossible for the site to really validate a well-disguised program that appears to be a user, because of browser sandboxing. The only info it has is perhaps timing information. E.g. let's generate 1,000 random numbers, throw them into a standard normal distribution to get numbers s₁ ... s₁₀₀₀ then use intervals of I_k = 40,000 + 5,000s_k, then use those numbers as the delays (in microseconds) between each keypress event. Looks just like someone hitting a key 25 times a second. So unless the programmer actually observed someone getting 14.5 on a trusted machine, and it wasn't just data that their javascript returned to the server (which by the way, the client can modify...), I'd take that number with a grain or two of salt.

In fact, thinking about it a little, even legitimately, 14.5 presses per second actually sounds like a rather low figure. Take a look at this video. It's part of a series in which devs are shown how speedrunners break their games. Here, a particular glitch only works on platforms where the framerate can reach 60fps (it won't work on consoles where the game runs at only 30fps). That tells me that the glitch (which relies on very fast button mashing) requires 30 button presses per second or more to execute.