Battery replacement for Inspiration 15 5559

Hi,

My battery has died and I want to purchase a replacement part for it from Dell site.

My original battery manufacturer no. is M5Y1K, while when I searched for a battery for 5559 on the Dell site, I could not find the same number, but I found only one battery with manufacturer no. HD4J0 which is said to be for 5559.

That is the product link:

Dell 40 WHr 4-Cell Primary Lithium-Ion Battery (Kit) | Dell USA

I do not know if that different manufacturer number will matter.

Thank you,