When I started, I spent $18 on one ad in a local paper. I had a 1/2T pickup, and a commercial Snapper mower in the garage. I got six customers from the ad, quickly picked up others to fill all my time. The mower went into the back of the pickup. I cut over 600 lawns for a portion of the first year, some over 1A. From there I expanded, added a trimmer, blower and a w/b. Somebody had a cheap 4X5 trailer to haul the w/b mower. Later, I added a larger trailer from somebody who was discarding, and later bought a larger trailer with landscape endgate. Later, I added a ZTR. It all started from the $18.
To the OP, spend your $5K on something else that has more potential. Business startups have an 80% failure rate within five years, and I am convinced that lawn businesses have a higher failure rate. Mowing grass requires no skill, no training, no special education, and the startup costs are very low. Or, stated differently, nearly ANYBODY can do the work, and your business offers nothing unique to the marketplace. You are just one of many doing the same thing. A high failure rate is almost certain with these factors.
To the OP, you need to ask some important questions, starting with "Do I want to be a business owner?" If so, then you need to ask "What kind of product or service does my business want to sell?" And, "What kind of customer do I want to have?" Passion for cutting grass and being outside are admirable, but they fall way short of the primary considerations of being a business owner. You mention college, so we can presume you hold a degree and have an educational experience that not everybody else possesses. Why not leverage this position? If your answer to the first question posed above about being a business owner, why not use your unique skills and education to build a business? Consider this position, over against those who have no skill, no training, or no education required to cut grass.
Just my $0.02 to the discussion.