What can I guess for this differential equation? What can I guess as a particular solution for $y''+25y = -x\sin(5x)$

I tried $(Ax+B)(C\cos(5x)+Dsin(5x))$, but that didn't work.
We need to use something similar to the right hand side i.e.
$${y_p} = Ax\sin (5x) + Bx\cos (5x).$$

Do you understand why?

If you do not understand why this is the way we guess, then try another but longer method. Take all the functions that appear in the product on the right hand side. Multiply them together and then simply put undetermined coefficients in from of each term.

If one of the functions is $\cos (ax)$ or $\sin (bx)$ then $\cos (ax) + \sin (bx)$ should appear in the product.
Here is a list of different combinations of functions for particular solutions.