If by "planetary boosts" you mean gravitational slingshot maneuvers, the biggest (absolute) delta-v you can get out of a slingshot is, I believe, twice the orbital velocity of the planet. (And that's only under certain conditions: you have to hit the planet head-on, and be travelling slowly enough to do the full 180-degree turn, given that your impact parameter can't be smaller than the radius of the planet.) Just one of those will probably send you out of the solar system. If you're lucky with planetary alignments, you might get two or three assists before absquatulating off into the vast abrupt, but not all of them can be head-on. Planetary orbital velocities range from a few km/sec to a few tens of km/sec, but .05c is 15,000 km/sec.
If you want to get a solar sail up to mildly relativistic velocities, you'll need a monstrous laser driver in the system of origin.
I learned a new word. My OED says:
absquatulate, v. (&b"skwQtju;leIt) Also absquotilate. [A factitious word, simulating a L. form (cf. abscond, gratulate) of American origin, and jocular use.] To make off, decamp.
183740 Haliburton Clockmaker (1862) 363 Absquotilate it in style, you old skunk,+and show the gentlemen what you can do.
1858 Dow Serm. I. 309 in Bartlett Dict. Amer., Hope's brightest visions absquatulate.
1861 J. Lamont Seahorses xi. 179 He [an old bull-walrus] heard us, and lazily awaking, raised his head and prepared to absquatulate.
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Absquatulating is not given but I suppose since it's a verb nobody can stop you from adding "-ing" to it.
--Boris
Thanks for the clarification.