Very, umm, shiny ...
The 65 in 195-65x15 is the tyre "aspect ratio" or "series", this is how tall the sidewall is compared to the width. A 65 series tyres, like you already have, means the sidewall is 65% of the tread width, or 65% of 195mm in your case. If you get new tyres on 17" wheels with the same "aspect ratio" or "series", then the sidewall will be the same height even though the wheels are larger; the overall tyres will be bigger than what you currently have, and it will stuff both the gearing (your car will have no pickup from standing starts) and the accuracy of the speedo (you'll get lots of tickets
).
195-65x15's have a 195mm tread & their sidewall is 65% of the height of their tread.
Sidewall is therefore 0.65*195 = 126.75mm.
Now, radius of a 15" alloy is 7.5", or 190.5mm.
So, the total radius of the new wheel+tyre must be close to 317.25mm.
Radius of a 17" rim is 8.5", or 215.9mm ...
So your new tyre must have a sidewall of 317.25 - 215.9 = 101.35mm.
Remember, the aspect-ratio or "series" comes from the tread width, so you need to know how wide a tyre you want to fit; depends on the width of the wheel itself.
Ratio = sidewall-height / tread-width
So if you choose 7" rims, you would use about 205mm tyres:
Ratio = sidewall / width = 101.35 / 205 = .494 ... this is dead-near .50, which is a 50-series tyre.
So with 7" rims, you'd go 205-50x17 tyres.
With 8" rims you'd be able to use tyres with 225mm tread width:
Ratio = sidewall / width = 101.35 / 225 = 0.450 ... that's 45-series.
So with 8" rims, you'd go 225-45x17 tyres.
Hope that makes sense.