To solve for p, first, add 2 to both sides of the equation
[tex]\begin{gathered} 2p-2=p+5 \\ 2p-2+2=p+5+2 \\ 2p=p+7 \end{gathered}[/tex]Now, subtract p from both sides of the equation
[tex]\begin{gathered} 2p-p=p+7-p \\ p=7 \end{gathered}[/tex]Therefore, the value of p that makes the equation true is
[tex]p=7[/tex]Verifying
[tex]\begin{gathered} 2p-2=p+5 \\ 2\cdot7-2=7+5 \\ 14-2=12 \\ 12=12 \end{gathered}[/tex]