Certainly! Here's your text with improved grammar:
On May first, my cousin and I played golf as we do every Thursday. When we approached the 7th hole, we faced a slight headwind. I usually hit my 5 iron, but today I decided to use my 4 iron due to the wind. I felt like it was a great hit, but the four of us never saw the ball. It was a 180-yard shot. I thought I hit the green, but I had no idea where it landed. As I got out of the cart with my putter, I noticed a ball on the green and thought it was mine. As I approached, another golfer walked up, placed his coin, and marked the spot. I said, "I thought that was mine." It turned out to be his ball. Still unsure of where my ball was, I assumed it probably went to the back of the green in the trap. I headed back to the cart to get my sand wedge. That's when I heard my cousin say, "You won't need a club, the ball is in the hole." What a shock! This was my second hole-in-one.