[cowsandmilk]

you're statement needs a lot of qualifications. It is in only very specialized cases where this is true.

Let's say my program takes time 1.0 and is made up of part A taking 0.5 and part B taking 0.5

Defining 5% speedup is weird in the first place, but let's say 5% speedup is taking 0.95 for the program and 10% speedup is taking 0.9 for the program.

5% speedup by improving part A => 0.45 + 0.5 => 0.95 runtime 5% speedup by improving part B => 0.5 + 0.45 => 0.95 runtime

making both improvements: 0.45 + 0.45 => 0.9

So, two speed-ups which individually would be 5% over the initial performance gives us a 10% speed up.

percentage speed ups do not necessarily compound. And in practice, usually they do not.