The sentence you wrote is almost correct! Here is your sentence:
"Elephants splash water on themselves using their trunks to stay fresh."
It's a good sentence! However, to make it a little clearer and easier for everyone, especially a 5-year-old, you could say:
"Elephants use their trunks to splash water on themselves to stay fresh."
This version tells us first what the elephants use (their trunks), then what they do (splash water), and why they do it (to stay fresh). It's a simple and clear way to say it.