An exact solution would involve math not completely trivial. Though, you can get a satisfactory answer by simplifying the case, because the decay times differ a lot.
432 years, 2 microseconds, 27 days, 159,000 years.
What happens to neptunium formed from americium decay?
From 2µs and 432yr, what is the proportion of neptunium versus americium, since you wait 5 years, much more than 2µs? From 27d ans 432yr, the protactinium versus americium?
You can go on to uranium, which accumulates, and evaluate its concentration over time - this one isn't a fixed proportion over americium.
The thorium concentration is quadratic over time over the year time scale, and radium cubic, as well as the followers up to 209Bi which accumulates. I'm not convinced you get one atom of 205Tl within 5yr with this chain.
- Is it Berkeley.edu that puts "Americurium"?
- Some computed concentrations will be so low that initial impurity will overwhelm them.
- If you have an electronics background, then all methods for linear systems apply: linear networks, fedback systems... Using fluence graphs, Laplace transformation and the like.
- If you have a background for linear algebra, you can write the set of linear equations with the formal s variable (Laplace transformation), solve, go the inverse Laplace.
- With 15 nodes, the general methods are not really accessible to hand solving. Either have a software that does it, and better, already knows all existing nuclides and decay modes - or go simplified methods by hand, as suggested previously.