I wouldn't regard that as a long time, it's pretty normal. She had probably just started work when the msg came through, she checked her phone after her shift. Or something. It's great that she replied to the icebreaker. But if she took 5hrs to do so, then as a safety precaution you should wait 5hrs before responding, just in case she was doing it to be manipulative. Generally they shape up pretty quickly if you do that, since the subcommunication is that you know what she's up to.
Also I generally wouldn't recommend doing any texting activity at all outside the hours of about 10:30am to 10:30pm as it makes you look thirsty if you text at strange times. There are exceptions to this, for instance you know her schedule so you call her around the time she'd be leaving work to ask her to meet you at some club. Or you met her same night so you know she'll be out till the early hours. But basically you want to look like a busy guy who needs his sleep at night.
For an example of
really long response times check out this interaction:
22/5 10:54 Me: [her name], enjoyed yesterday? Interesting fact: my neighbour is from Osaka [this girl is from around there]. we went clubbing, came for some coffee and did some Osaka dialect practice, it was good. Your plan also went successfully?
25/5 11:44 Her: hahaha (funny face smiley)
Is that right! Since we live close together let's go for a coffee or something!
26/5 13:10 Me: Bubble tea, Thursday evening, convenient?
Basically, I knew she was FOS because she took so long to reply, so I invested as little as possible to see where we stood, and sure enough, no further reply.
Ray