At the very end of The Fifth Element, Korben and Leeloo are stripped and placed in some kind of healing device. Is this strictly for medical purposes, or are we to believe that they engaged in sexual intercourse?
Yes, if you consider that "kissing and probably engaged in hoppi hoppa" is sexual intercourse.
Here a quote from the script:
283 INT. LABORATORY We are in the Nucleological Laboratory that gave birth to Leeloo in the beginning of our story. The President enters the lab followed by a group of officials in ceremonial dress. MUNRO Mr. President, let me introduce you to Professor Mactilburgh, who runs the center. MACTILBURGH It's an honor to receive you. Mr. President. PRESIDENT (beaming) Yes.. Well? Where are our two heroes? MACTILBURGH They were so tired from their ordeal that we put them in the reactor this morning.. PRESIDENT I have 19 more meetings after this one Professor.. PROFESSOR Of course.. Let me see if they're revived. AIDE We go live in one minute, Mr. President. Mactilburgh goes to the reactor and opens a small slot which allows him to see what is going on under the blue shield. Leeloo and Korben are naked, arms wrapped around each other, kissing and probably engaged in hoppi hoppa. Mactilburgh looks troubled. MACTILBURGH I.. uh.. they need five more minutes, Mr. President.
In an other part of the script, they confirm exactly what is hoppi hoppa :
KORBEN You learned 900 languages in five minutes?! LEELOO (pleased) Yes! Now it's your turn! I learned your language, you have to learn mine! KORBEN I know how to say "Hello". Teach me how to say "Good-bye", that's all I need. LEELOO Apipoussan! KORBEN Apipoussan? LEELOO Good! Do you know how we say "make love"? KORBEN (fumbling) Uh... LEELOO ...Hoppi-hoppa.