power of five

Powers with brackets, addition and multiplication
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative


Find the value of $x$ so that:

$$5\left(5^x+5^x+5^x+5^x+5^x\right)^2=5^9$$

This problem is adapted from the World Mathematics Championships