Tube tire suggested pressure

Finally got both tires on my 305 and holding air, and I noticed on the left peg/muffler bracket a suggested pressure of 27psi front and 25psi rear. It's rideable, but feels very sticky - a lot harder to turn than my 750, which I run 42 front/rear on.

Am I okay to bump it up to maybe 35 or so? The tires I'm using are tubeless-type, so they can handle it, and I know that the tubes can hold at least 90. Just thought it should feel more nimble.

What tires?  Did you look on the manufacturers website to see what if any pressures they recommend?

Web search on this topic found this excellent tidbit...

How to ensure your tires are properly inflated

Start with the motorcycle manufacturer's recommended pressures. Do not exceed the tire manufacturer's recommended pressure. That value is printed on the sidewall. Now that you have your boundaries, I recommend using the 10% rule to dial in the correct pressure for your riding style and your bike. Consistently using the same tire pressure gauge which you have deemed reasonably accurate, check your tire pressures when they are cold. After you have ridden a bit and have gotten them up to temperature, one of your normal rides, stop and immediately check the tire pressures. Don't wait too long after you stop to take the readings. Do it before you even take off your helmet.

If your cold tire pressure was correct, your hot tire pressure will be approximately 10% higher than your cold tire pressure. If your hot tire pressure is more than 10% higher than your cold tire pressure, that means your side walls are flexing too much because your cold tire pressure is too low. If your hot tire pressure is less than 10% higher than your cold tire pressure, that means your side walls are not flexing enough because your cold tire pressure is too high. Next time your tires are cold, make the necessary adjustments and repeat the exercise. The results will vary depending on whether you are riding solo, two up, solo with gear, interstate or twisties, summer or winter, high altitude or sea level. Eventually you will end up with a reference log for the different conditions.

If you do this, you will optimize the combination of tire life, performance and gas mileage.

By ghostdive:  .... a lot harder to turn than my 750, which I run 42 front/rear on. ....

42 psi sounds high to me.  Is that the max listed on the tire?

You probably aren't going to get a definitive answer about what tire pressure to run. 
The OM says 25 psi, which seems low to me, so I go with a pressure between that & the max embossed on the sidewall.
Out of curiosity I tried the max on some Dunlop 501s, but it felt like riding on glass.  

42 is the max for my Pirellis on the 750, always felt fine and haven't ever had any traction issues.

I'll check the max on my Dunlop 404s and give it a shot. I guess I just thought that maybe the pressure listed on the bike might have something to do with running tubes, but it may also have been the max pressure for the stock tires 40 years ago...oh well!

You should NOT run the tires at the max pressure rating as listed on the tire.  That's for a highly loaded situation, not for normal riding.  

You'll have to figure out what works for you based on experimentation.
The tire compounds now are different from when your bike was made.
So the factory specs might not be ideal with today's compounds.
The factory pressure numbers are a good starting point though.
Within the range up to max pressure it's almost a preference thing.

DoctoRot posted a good video from Dave Moss explaining how to find the ideal pressure.