Some databases on the NEHGS site (americanancestors.org) are viewable to the public but this is one that is for members only. (If you have New England ancestry, this web site is a steal.) If you are a member, you can enter your possible ancestor's name in the Database Search box and hope a silver book entry turns up, but if your ancestor's name was a common one for the 1700s, you might go to the Database pulldown menu (just above the blue box marked "Search Tips") and select "Mayflower Families Fifth Generation Descendants, 1700-1880."
If your person does not show up, be patient. They have digitized roughly 4 shelf-inches and have another 30 to go, by my estimate. If you cannot wait that long and you live in Arizona, the state society's web site (arizonamayflowersociety.org) lists the 6 libraries to which the state organization has donated a full set of the books. Click on "membership" at the top, then select "resources." There is a downloadable list of libraries. The state Society also owns a set. If you live elsewhere, try worldcat to search for a repository near you or contact your state Mayflower society. Contact info for state, Washington D.C., Canadian, and European societies are on the GSMD web site under the "Join" heading at the top.
A word to the wise - which is YOU: Do not ever use some digitized version of a silver book that you found online. Genuine digitizations are ONLY available via the NEHGS partnership. Now and then a castoff volume, long outdated and often one of the early "work-in-progress" paperbacks, is put on the internet. They are no longer accepted because they contain inaccuracies, including disproven family legends, and they are missing whole families since proven to be descendants of your pilgrim. You may not cite these on your application. The GSMD accepts only the current version and the state Historian (who helps you with your final application) has a full set if you do not. You do not need to reprove facts already published in the silver books.(So please do not mail your state Historian photocopies of pages from these books!)