This is unusual for numbering. Usually in most counting systems, one would employ the decimal method. So it should be 10+5 Bishvat. But note that 15 is not written "yud-hey" (10 + 5) because Yud Hey is one of God's Hebrew names. So that we don't use the name of the Almighty in a pedestrian (or vain) way, we use 9 + 6. Clever.
The meaning of the holiday, that is, the purpose of the celebration is that we note the "new year for the trees" since this is the beginning of the agricultural cycle in Israel. When I was a kid, this was a time to raise funds for tree planting in Israel. We would shake a can at old people and ask them to contribute so that we could plant a tree in the Holy Land. Not that as a youth I ever made it to Israel, but the money collected went to the synagogue and I imagined that the money did pay for some trees.
Tu Bishevat is the new year for the purpose of calculating the age of trees for tithing. See Lev. 19:23-25, which states that fruit from trees may not be eaten during the first three years; the fourth year's fruit is for God, and after that, you can eat the fruit. Each tree is considered to have aged one year as of Tu BiShvat, so if you planted a tree on Shevat 14, it begins its second year the next day, but if you plant a tree two days later, on Shevat 16, it does not reach its second year until the next Tu BiShvat.
Where there is a law, there are lawyers, loopholes and more laws, so don't be surprised at this reckoning.
But let me get back to the 9 + 6 rather than the 10 + 5. I like that the legal minds of Judaism put a fence around the name of the Lord, so that we wouldn't use it for ordinary use. I appreciate their zeal for preserving the dignity of the name. At the same time, I think they might have missed an opportunity to highlight God's presence on the 15th of each month.
In the same way we put his name "El" in names of children and cities by attaching it as a suffix (Nathaniel, Ezekiel, Yechezkel, etc), where we almost invoke his name, we could be doing that each month on the Yud-hay of the month. After all, many Jewish holidays fall on the 15th (Passover, Purim, Sukkot) and we don't shy away from using the fullness of the moon to help us note those. Yud Hay Shevat would be a great way to remember that God gives us nature, especially trees, and asked us to keep track of their ages.
I like giving myself a chance to put God into the conversation, and into memorial places in my life. No matter what else you are doing today, take a minute just now, and ask God to be in your day, to guide you, and to strengthen you to His tasks. Sound like a plan?