According to some reports a human can survive at up to ~5 gravities
Humans can survive well over 5 gs for briefer periods. In nominal orbital flights crews have taken over 7g on ascent for short periods of time (Titan-Gemini) and higher forces very briefly on reentry.
From Earth it takes about 10 minutes to get into orbit; we can expect it would be a bit longer to ascend from a high gravity planet, so the limiting case would be what force a human could sustain for a few hours: enough time to descend, get out of the spacecraft and plant a flag, and return to orbit.
From the charts given in another answer on this site, it looks like 5g for 1000 seconds is tolerable "eyeballs-in", i.e. with a crewman on their back, and nearly 4g "eyeballs-down", i.e. standing on a planet's surface.
Any ascent has to be carried out at generally higher acceleration than the planet's surface gravity (though some launch trajectories do have brief periods of < 1:1 TWR, such as the space shuttle just after the SRBs burn out), and the lower the margin, the longer the ascent takes and the larger the launch vehicle has to be in proportion to its payload.
Given these constraints, it seems feasible to lift off from a planet with 3g surface gravity in a rocket with an initial acceleration of 4g, which maintains acceleration between 3g and 5g all the way to orbit through a combination of staging and throttling. A little higher surface gravity might be workable also.
Note that a rocky planet with 3g surface gravity is expected to have a very deep and high-pressure gaseous atmosphere, which will complicate both astronaut survival and launcher/trajectory design, so the practical limit is certainly quite a bit lower.
other reports suggest launching from > ~2 gravities might not be possible with rocket engines.
It should be theoretically possible, it's just that the payload mass ratios become extremely poor, meaning that you need much larger rockets to get even small payloads into low orbit. Depending on your engineering assumptions, for a one-crewperson spacecraft launching from a 3g planet, you need a rocket about 20 times the size of a Saturn V. Structural engineering issues also complicate the design of rockets this big; for example, finding enough room on the bottom of the rocket to mount all the engines you need at liftoff runs up against square/cube scaling problems.
So we might colonize a planet with higher gravity, but never be able to leave.
I believe that any gravity you can colonize (i.e. tolerate for an unlimited amount of time), you can leave (i.e. sustain a slightly higher g-force for a short period of time).