Does the Samsung Galaxy S 10.5 have the hdmi connection capability?
It does, but you'll have to experiment to find out which adapter will work on it, or you'll have to buy the Samsung adapter (about $60). (Android devices have MHL output - you need an MHL-to-HDMI adapter.)
The Note 10 (I don't know about the 10.5) can mirror using Chromecast. (And, of course, any Samsung device can mirror to a modern Samsung TV.)
But the difference between a laptop and a tablet is a lot. A laptop, even a cheap one, gives you a LOT more storage, full programs, not just for office documents, a better keyboard if you're going to be doing more than texts and emails (watch the increase in carpal tunnel syndrome cases in a few years, as millions of people type for hours on a tablet without an external keyboard), more interfacing (e-Sata, more USB, automatic USB host mode, externally available card reader on many of them, easy to connect a larger screen or even a huge TV, easy-to-replace battery if you ever need to, etc., etc.) And with current devices, you get a lot more CPU power and a lot more RAM in even a cheap laptop than in an expensive tablet (and that counts for multitasking and speed).