This is a very good question. There's lots of different reasons, depending upon your needs. If you have, as you said, been using Classic **** with no problems ****, then there may not be any need to switch to TW5. However, most people have had problems with TWClassic because TiddlyWiki runs within the browser and it's ability to save changes have been affected by browser technology over the years. Most significantly, nearly all modern browsers have become much more cautious about security and privacy issues, and as a result, local file I/O functions have been *removed* from most browsers.
Although TW does have a default "download-to-save" function that is supported by most browsers, the workflow it creates can be a bit confusing and error-prone. The alternative is to use some kind of browser-specific add-ons or local applications that provide a run-time environment for TW to access the needed file I/O functions. Depending upon your syem setup and your specific needs, installing one of these alternatives can be even more confusing and error-prone.
Another big hurdle to switching to TW5 is that the old TWClassic wiki syntax is only marginally supported and NONE of the existing TWClassic plugins will work in TW5. Fortunately, TW5 provides a much more powerful set of native "widgets" and "macros" that incorporate many of the features that were previously provided by plugins in TWClassic. Though it takes a bit of effort to learn the new syntax and techniques (filters, lists, transclusions, templates, etc.), switching to TW5 can be incredibly rewarding.
-e
Eric Shulman
TiddlyTools.com: "Small Tools for Big Ideas!" (tm)
InsideTiddlyWiki: The Missing Manuals