Immediately on waking drink a glass of water. That will help you wake up. I also suggest drinking a large glass of water before retiring, in about 4 hours you'll need to get up. That's one way of waking up. If you prefer to sleep then drink the water on awakening. Dehydration is one of the reasons we are drowsy on waking up in the mornings.
Also consider that you might need more than 5 hours sleep. Shorten your meditation period to say 15 minutes and work backwards to the hour. So wake up 20 minutes earlier than normal go to the bathroom then do 15 minutes mediation. Do that for 3 or 4 days. Longer if it's a struggle, then add 10 minutes so wake up 35 minutes earlier then meditate 30 minutes. A week or so of that add another 15 minutes to your meditation and get up another 15 minutes earlier.
In all first thing on waking, drink a glass of water. If you tend to be drowsy on waking, you're probably dehydrated. Make sure you're sufficiently hydrated by day and you sleep better and wake up more refreshed.
Alex