Okay so the electron configuration is [tex]1s^{2}2s^{2}2p^{5}[/tex]. Look at the periodic table. There are 2 blocks you need to know for this question: the s-block, which is comprised of groups 1 and 2, and the p-block, which is comprised of groups 13 through 18. Because your configuration ends in [tex]p^5[/tex], your element has to be in group 17, a halogen. Now, you need to know another thing - your s sub-level has 1 orbital and your p sub-level has 3 orbitals. Every orbital can fill up with 2 electrons. Now, the fact that the configuration ends in [tex]s^{2}...p^{5}[/tex] tells you that the s-orbital is filled, and your p sub-level is not completely filled. If it was, you would have 8 valence electrons, and it would end in [tex]p^6[/tex]. Now, because it ends in [tex]p^5[/tex], it has one less valence electron, so in your element you have 7 valence electrons.
17-10 add 3 and minus three divide by two and multiply by two and that is your answer which is seven
