.
Sorry, not all the tutors at this forum are familiar with the abbreviations you use in your post.
The rule of a politeness in Math (when you come to the scene) is to speak in understandable (or commonly accepted) language.
//////////////
My solution is below.
Let x be the number of LPN.
Then the number of RN is (x+5) now, according to the condition.
The product of LPN by RN now is x*(x+5).
The product of LPN by RN 5 months ago was (x-5)*x.
From the description, you have this equation
x*(x+5) = 3*(x-5)*x
Cancel x in both sides
x+5 = 3*(x-5)
Simplify and get the answer x= 10.
Solved and explained.