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The key is to gradually build up to 5 kms (and beyond), rather than smashing it and getting injured. Intersperse running for a period with walking, so start with 1 minute running, 2 mins walking and gradually increase the running periods and decrease the walking. I did this about 18 months ago and have been, touch wood, injury free so far.
As @Wrongcog said, you've got the aerobic capacity to run, but you don't have the strength, particularly in your ankle, knee and hip joints. You need to build that up before you can run properly.
Pain as in very achey muscles really. But kind of to the point that when sitting down I'd come to a point where I had to let myself crash down..! 😂 So as you say, it was probably a case of my body/muscles not being used to it and therefore taking a hit.
Will definitely consider starting some strength training as I've found it was the key for me to up my cycling while remaining niggle and injury free after my knee gave me some grief initially.