Can you return two of the chairs? Then get a couple narrower chairs. They just have to harmonize, not match. They could be the same color as the ones you have or matched to the tabletop.

Helix Rustic Wood Dining Chair Set of 2 · More Info

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I would push chairs in as far as they comfortably go. I was just noticing that the seats are not completely under the table and still reach nearly to the center column. They may be extra deep as well as wide. That would also make the table seem smaller. I pulled up Wayfair to check chair sizes and they have several styles similar to what you have chosen but with an 18" width. You might want to look there if you want something similar to the wider ones.

Take good measurements before you buy, especially how wide the chair legs splay out. I just noticed that the legs on the second chair spread out sideways.

I have a 60 inch round kitchen table as well. We are also a family of 5 and I only keep five chairs around the table. We have been up to 9 people around that table though. Look at Crate and Barrel Lowe chair. That's what I have and I love them. I just wipe them down and nothing stains or shows. Great with kids.

That table doesn't look 60" in diameter. I have a round table that extends to a 62" oval with leaves. If it were 60" in all directions, 6 chairs would be no problem.

Photos can be deceiving but i agree with the others--make sure you got the correct table delivered!

Funny I’m actually trying to put 6 chairs around my 60 inch table now and I have a similar table it’s the darn table legs in the way
My chairs are definitely narrower but the backs were to high for my area ,so I had them shortened
Table issues 🙃
I do believe your chairs are a tad wide so return if you can and buy narrower ones as it will always bug you
If not ya switch out a few mix it up

Go up to a 72 on the table if you have the room!