We have this problem at work every time the painters come through. Do not be tempted to hit the frame with a hammer as this will crack the glass (personal experience).
Personally I have used a paint scraper or putty trowel (best) and at other times a bread and butter knife to wedge between the sliding part and the frame and slowly worked my way around the edges. At times I've had to tap the trowel/ knife gently in using a hammer.
Start in one spot and work your way around. Often it will crack the paint ahead of you. Once you get it open you will find the more you open and close it the more paint gets knocked out of the way and the easier it is to open. Remember windows have two sides and be gentle. - JDE
I recommend breaking the paint bond in the corner where the sliding window begins and meets the edge of the window frame. I suggest using a Stanley Knife. Please be careful not to cut too deeply or you will damage the timber frame.
Once you've broken the paint bond, you need to induce movement, I recommend using an Ozito 2000W Variable Temperature Heat Gun. The heat of the gun will do two things. First, it will soften the paint, allowing you to shake the frame loose. Second, it will dry off any excess moisture that's in the wood, thereby shrinking it and allowing you to loosen up the frame. The heat gun kit comes with a paint scraper. Gently insert this into the gap of the timber all around as you gently pry the frame loose. Make sure that you shoot it with the heat gun while using the scraper.
Please note that putting the heat gun on a very high setting will soften and peel the paint. And don't forget your personal protective equipment such as gloves and eye protection. - EricL
Here is a last resort idea: if you have a multi tool, you could cut along the painted edges of the windows to separate the painted joints. You shouldn't have to go in very deep. I think the Stanley blade would do the trick. - JoeAzza