Double clutching is generally not something you would want to do when upshifting because you are raising engine speed when you do this. This is what you want for a downshift, but not for an upshift. My guess is you're doing this because when the engine speed drops too low for 5th gear, you're having trouble completing the shift.

It is not uncommon for many manual transmissions to have stronger synchronizers in the lower gears than in the higher gear because those are the ones that are most commonly used. What you're describing sounds to me like your 5th gear synchronizers are worn. Either that or the blocker rings are damaged. In order to try to minimize your problem, note the RPM difference between 4th and 5th gear and try to make sure that when you upshift, you are at that RPM for 5th.

As for "..double clutching is highly not recommended on the newer cars", this is not true at all.

 

like everyone said practice. but "roll in and out" of the throttle when your trying to get used to a stick shift. it's a tough technic at first to get but once you get it like second nature.