Any would be appreciated! i'd like to understand it, so an explanation would be nice. you.

From the second equation,we get y=x+2
substituting this value of y in first equation,it becomes

x+2=x^2+5x-3
re arranging,we get
x^2+4x-5=0

using the method of splitting the middle term,we get
x^2+5x-x-5=0
x(x+5)-1(x+5)=0
(x-1)(x+5)=0

from here we get two values for x
x=1 & x= -5