If we plug the values, we have
[tex] f(2) = 2p+3,\ g(5) = 5+4p [/tex]
So, we have to solve the following equation:
[tex] 2p+3 = 5+4p \iff -2p=2 \iff p = -1[/tex]
So, when we impose [tex] f(x) = g(x) [/tex], knowing the value of p, we have
[tex] f(x) = -x+3 = x-4 = g(x) [/tex]
And so the solution is
[tex] -x+3 = x-4 \iff -2x = -7 \iff x = \dfrac{7}{2} [/tex]
