I got a new GPS for my Matek f405, and after I set it up and got betaflight to recognize it, I can't get any satellites. It's a BEITIAN BN-220T.
The GPS module can't give you even an approximate position fix until it knows where the satellites are. The satellites transmit this data (called an "almanac") continuously, but it takes about twelve and a half minutes to send a complete copy, and it's only good for a few weeks. If your GPS module has been powered down for longer than that, it needs to wait for an updated almanac before it can do anything.
(Your cell phone can get a faster fix by downloading a copy of the almanac off the Internet, but presumable your quadcopter isn't set up for this.)
I'd say if you get any satellites at all, the GPS module works and it got the almanac correctly. Getting only 5 sats after 10 minutes is indeed insufficient (8 is fine though).
It could be that this particular GPS module is not good enough, or it simply doesn't work very well at your flying site. Nearby trees, buildings, or even parts of your drone can interfere with GPS reception. It's also possible that glitches on the power supply line make the module reset periodically, so it never gets into stable operation.
Try finding a place with no obstacles around (a field outside the town) and make sure it's supply voltage is stable.