Q.Need help before pruning lilacs
I recently moved to a house in Western NY with a row of 5-6 very old and very tall lilacs that have not been taken care of in many years. They are blooming, but the blooms are so high up that we can barely see or enjoy them. I have absolutely no experience with gardening, as I used to live in an apartment in NYC. I have read several articles on pruning lilacs but I still am uncertain what to cut, how to cut it, and what to leave. I would rather not do a drastic pruning. Do I cut some of the stems all the way down or cut many stems just to a desired height? Some of the bushes have shoots that look like they’re growing out of the ground near the base of the bush. Should I cut those or leave those as new growth? I attached a picture just to give you an idea of what the lilacs look like. Any advice is welcome!

Here are some articles that will help you prune your large overgrown lilacs. You can revive your lilacs through either renewal pruning or rejuvenation pruning, both of which are explained in the article below. Since you are not looking to do a drastic pruning you can opt for renewal (done in phases) instead of rejuvenation: https://www.ipm.iastate.edu/ipm/hortnews/1993/2-10-1993/lilac.html
Hacking & Whacking - Dealing with Overgrown Shrubs (has a photo of rejuvenated lilacs):
https://extension.psu.edu/plants/green-industry/news/2012/hacking-whacking-dealing-with-overgrown-shrubs
Pruning Lilac Bushes: When To Prune Lilac Bushes:
https://www.gardeningknowhow.com/ornamental/shrubs/lilac/pruning-lilac-bushes-when-to-trim-lilac-bushes.htm