My bike came with a decent carrier rack when i got it about a couple months ago but the only problem is the top two screws closest to my seat post just wont budge, i've tried using different screw drivers and one of the screws got stripped a little bit. I'd really like to be able to use panniers instead of my messenger bag

Screw head is now too beat up to cooperate with a screwdriver? A screw exractor is one option. https://www.acehardware.com/family/in...goryId=1259460
It's not a hex head screw, is it?

Are you removing a rack? Or, just adjusting it?

I've actually yet to attach the rack, the extractor kit looks good. It similar to a regular phillips screw but the outside of the head is shaped like a hex bolt but very thin.

is this a New bike or a "New To Me" bike? if it is a brand new bike take it back to the shop and have them look at the screw. Also if you are unfamiliar with tools like a screw extractor I highly recomend you take the bike to a shop first. using a extractor ona 5mm screw is a bit tricky because you need to be very precise with drilling the hole for the extractor to go into.

Did you try a wrench? it is likely a 8mm and I would try a wrench using my left thumb to try and keep the close end of the wrench from slipping off. careful use of visegrips may work too

put the tool into the hole and smack it with a hammer a couple of times. can help break loose any corrosion or scale on the threads.

If all else fails grind the head off the screw with grinder on a drill. When the head is off you can simply use a pair of pliers to remove what is left of screw

Try applying penetrating oil to the screws and let it sit for a while, maybe overnight, before trying again to remove them. I prefer Kroil but Liquid Wrench is more generally available. As Bill in Houston mentioned impact may help loosen things up and should be done after applying the oil to help it penetrate the threads, then also while trying to remove the fasteners. Mild heating, short of damaging the paint, may also help.

Are you sure it's not an Allen screw that you're mistaking for a Phillips?

Kroil + overnight

I frequently encounter hard to remove screws when dismantling motorcycles. A buddy of mine in Mesa, AZ who is an aircraft mechanic recommended a 50/50 mixture of acetone and anutomatic transmission fluid to help loosen the most difficult ones. The acetone thins the ATF to a point that there is a capillary suction phenomenon that draws the mixture into the threads. ATF, when allowed to sit for a while, will work wonders on rust & corrosion. I typically apply it and let it sit for a day or two before taking a hand-held impact to the problem. I rarely have to give one a second dose of the mixture to get the job done.

impact screwdriver. if they are stripped hex i use a "sock it out"

crusinintx's suggestion may have merit, but apply such a mixture with caution as the acetone may strip your paint. Commercial penetrating oils do a good job of creeping into joints ( Kroil = KReeping OIL) if you give them time to work.

People find it hard to believe, but left handed twist bits, (reverse the drill!) used in the extractor scenario, will often break out the threaded section of bolts or screws. A right handed bit drives it tighter.

+1 My easy out set came with LH drill bits. Often the bolt comes out in the drilling process.

if it's stripped, instead of buying a screw extractor (quite pricey) and possibly damaging your bike just take it to your LBS. Labor costs would be minimal, hell, they might just do it for you for free.