Nope, don't change the router IP. Actually the pic you added shows your DHCP range is 192.168.0.100 to 192.168.199. So you can use any IP in the range 192.168.0.2 to 192.168.0.99 as static.
So for your ESXi host, try this:
IP 192.168.0.5
Subnet mask 255.255.255.0
Default Gateway 192.168.0.1