Yes. they don't check boarding passes unless you look totally lost and need assistance. The only issue here would be if you had luggage to recover at T3, since that won't be transferred to T5, but if HBO or through checked to somewhere beyond LHR then I see no issue. I often use T5 Flight Connections to get to T2 if I'm in a Bath Road hotel overnight, it's easier to get to the Bath Road TfL buses from T2.