I am leaving on a 5 week vacation. It was suggested that I shut off the water to the house
And do the following; Shut the main. Drain the water from the sinks etc. in the house. Leave open both the hot and cold water faucet in the basement laundry sink. Is this procedure OK. Also, what procedure should I follow when returning home and turning the water back on? Thanks

Sure is a good idea... do exactly as you said... and if you have a gas water heater I would turn the thermostat on front of heater to VACATION mode... if electric water heater I would turn off the breaker or fuse as well.

Then when you return just reverse the order... close valves, turn on main shut off, purge all water lines (means to just open them all... start at the tubs first... less likely to clog anything else in house) and then turn up heater or turn on breaker to heater... that should do it.

Sometimes when you shut water down like this you will end up getting reduced pressure to a sink or two when turned back on... but that is usually not a big deal... if you did will probably only be clogged aerators... no big deal just loosen them and clean them out. And, of course, if any issues come up when you return just let us know. I am sure someone on site can help!

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Congratulations! Turning off the water when you leave on vacation is the cheapest insurance that you'll ever buy. Will you be shutting off the heat when you leave? If not then the above advice doesn't go far enough. Water heater, traps, etc.
If the heat will be shut down then you will have to winterize your home before you leave. Where do you live and how cold does it get. Will you be coming to Florida on your vacation? It's been running in the 70's here lately. After X-mas and we're still running the air most every day. Regards, Tom