I don't think it should really matter if you leave the airport on transit. As long as you have the boarding pass and your passport, I don't see any problem getting back in. Unless you need special visas and such that we might not know about.

Singapore:
5-7 hours is a lot time.

I've read of post where people who live in Singapore would go home and unpack their dirty clothes, and do their laundry and make it back in time for their connection.

That said you can go downtown and shop.

FRA:
I've take a train to the city to have a meal before, but that transit was a little more than 7 hours.

Think the train took less than 30 minutes (travel time) to downtown. It was a matter of walking around and finding the best thing to eat

But alot depends on your arrival time for both airports. i.e:If you arrive at 5 am and leave at noon it maybe pointless.