No, not quite: you need to say more about what $p$ denotes.
The one change you need to make is denoting, by $\;p,\,$ "the front **door is closed.** " I'm assuming this is what you meant $p$ to represent.
Then together with $r:$ "the back door is closed", and $q$ "the light is off", your translation is then correct: $$(p\land r) \rightarrow q$$