Your LEDs have a forward voltage range from 3.0V to 3.5V so the average is 3.25V.
17.5V/5= 3.5V which is the normal maximum forward voltage for a modern white LED. If its operating power is 1W then its operating current is 1W/3.5V= 286mA, not 1.75A. If the typical forward voltage is 3.0V then their operating current can be 1W/3.0V= 333mA.
An average LED with a forward voltage of 3.25V can operate at 1W/3.25V= 308mA.
In your first post you said the LEDs can operate at a current of 350mA then their power rating must be higher than 1W.
We are talking about having 5 LEDs in series so the current is typically 308mA, not 1.75A.
You are talking about 1.75A so maybe your LEDs are in parallel (350mA x 5= 1.75A).
If your LEDs are in parallel then the one with the lowest forward voltage will draw much more current than the others and will burn out soon. Then the remaining LEDs will burn out soon. The power supply voltage needs to be much lower, about 5.5VDC, not 17.5VDC.
Since your LEDs are in parallel then a linear driver wastes (17.5V - 3.25V) x 1.75A= 25W making heat.