Answer :
If [tex]x=p+2[/tex] and [tex]y=p-3[/tex], then
[tex]x+y = (p+2) + (p-3) = 2p - 1 \implies x+y+1=2p[/tex]
and
[tex]x-y = (p+2)-(p-3) = 5 \implies x-y-5=0[/tex]
as required.
If [tex]x=p+2[/tex] and [tex]y=p-3[/tex], then
[tex]x+y = (p+2) + (p-3) = 2p - 1 \implies x+y+1=2p[/tex]
and
[tex]x-y = (p+2)-(p-3) = 5 \implies x-y-5=0[/tex]
as required.