My saliva ranges from 5.5 to 6.5 throughout the day, even after brushing, drinking water, eating veggies. It is not good for my teeth.

I am sucking on a Xylitol mint that has probiotics as well to replace the acid loving bacteria with other healthier ones form y mouth.

How can I make my saliva more basic / alkalize it?

Salivary pH can change depending on what foods are being eaten, but it is generally bacteria in the mouth that create most of the mouth's acids.  

My first recommendation is to switch toothpastes to one that does not have added sweeteners.  Auromere makes several very good natural toothpastes with herbs that also help to kill off bad bacteria in the mouth.

Another thing you can do is to get zinc tablets and suck on them.  They don't taste very good but they will kill off the bacteria and also make great breath fresheners.  Don't exceed 50mg total daily of zinc though, and remember to have food in your stomach when doing this to prevent nausea.