Question

What is my equation

Answer 1

So you can award a Brainliest to the other person answering this, you need to solve this for x = 7

f(x) = 5 ^ x
f(7) = 5 ^ 7
f(7) = 78125

Answer 2

This is pretty obviously

$f(x) = 5^x$

If it wasn't obvious we can find the common ratio r by dividing successive values:

5/1=5
25/5=5
125/25=5
625/125=5

That's the common ratio.  We multiply by the first term, but the first term is one, so that has no effect.

$f(x)=5^x$