I think it is simply that she is waking up at the end of one sleep cycle. It is common for babies to wake up (actually adults do too!) at the end of each sleep cycle. You can try to encourage her to go back to sleep rather than to play after the end of the first cycle. Try doing things that you have been doing (e.g., feeding, rocking, holding). Sing or talk softly to calm and soothe her back to sleep may help too. You can also try having someone else (daddy perhaps?) to put baby back to bed. Usually babies are just looking for comfort and would slowly learn to soothe themselves back to sleep as they develop.
I'd suggest setting a bedtime routine to set boundaries and to let baby know that it's sleep time and perhaps she'd sleep throughout the night instead of treating bedtime like a nap, waking up sporadically. Maybe start with a bath, a diaper change then into her pyjamas, and maybe a story or song. Instead of letting baby fall asleep in your arms, put her to bed when she starts to show signs of bring sleepy. Finish the bedtime ritual in your baby's bedroom and make sure that her room is a pleasant and conducive place to sleep.
This happened to me too! For a time, my baby decided that 2am was a great time to play and poop. Needless to say, this drove her co-sleeping parents nuts! She grew out of it though. I think it was from a change in rhythm when we went for a family trip and she got so tired from being out all day that she slept so well and so long at night. When we got back, she lost the 2am habit.
Has she always been this way, or is it sleep regression? If it's something recent it could be because of teething. At 5 months a baby can sleep for 10-11 hours a one shot. How many hours does baby sleep in the night (in total)
Heavier meals before bed
Heavier meal b4 sleep