Redirect all traffic from multiple interfaces to single IP

Link at the bottom of your question is aimed at people who have multiple exit IPs. Since you are trying to push packages through eth0 (192.168.1.5) - you don't have IP aliases and you don't have multiple exit IPs but a single IP.

So, lets say ppp0 has ip range: 10.100.100.0/24, initial packet connecting to your host will look something like:

 | SRC IP        | DST IP       |
 | 10.100.100.10 | 10.100.100.1 |

Your first rule is correct:

-t nat -A PREROUTING -p tcp --dport 5000 -j DNAT --to-destination 192.168.1.10:5000

So, whenever a machine behind ppp0-ppp3 tries to contact your host (192.168.1.5) on port 5000, packets will get re-routed to 192.168.1.10. Packet will look like:

 | SRC IP        | DST IP       |
 | 10.100.100.10 | 192.168.1.10 |

Now, you're routing packets through your host, so you have to enable IP forwarding:

sysctl -w net.ipv4.ip_forward=1

But, when destination (192.168.1.10) gets packet, it will see source 10.100.100.10 and it will return packet to his own default gateway. What you can do is set up static routes on 192.168.1.10 that will tell that host that packages originating from 10.100.100.0/24 are routed via 192.168.1.5, something like:

ip route add 10.100.100.0/24 via 192.168.1.5

This way, you wouldn't need to add any POSTROUTING rules, because destination (192.168.1.10) would automatically know where to return packets.

But, if that solution isn't viable for whatever reason (or you personally don't like it), next thing what I would suggest is to use MASQUERADE on eth0:

iptables -t nat -A POSTROUTING -o eth0 -j MASQUERADE

DNAT solution will also probably work. Just make sure your FORWARD chain is set to ACCEPT and not filter packages on their way through your host.