Any time you have any issue with basement moisture the first thing to do is to make sure ALL downspouts exit FAR away from the foundation walls (at least 8-10 feet ideally) and that the grade is sloping AWAY at least 6 inches in 10 feet.

Water can flow into weird spots and you won't know unless you do a lot of expensive digging. Makes a lot of sense to fix cheap things first and in many times this will fix the problem.

Unfortunately we don't have the space between our house and neighbors to have the downspouts that far from house, unless we dump water into their house. Also we are on a hill and yes I agree ideally making sure the land slopes away from house is ideal but unless we change the whole back yard and dig up the crawl space then I don't think we can do that. We are trying to come up with ideas for the downspouts that are close to the house but having a hard time since we have about 2 ft to work with . Poor planning of the house unfortunately.

Is the hill sloped TOWARD your house? If so, you've potentially got bigger issues.

If you are that close to your neighbor you either need to swale the space or run drainpipe underground to exit to daylight somewhere else. You can't have downspouts exiting that close to your foundation and not have problems eventually.