J.,
Hi. You have a tricky situation here. It sounds like both the girls are calling out for attention. First, pull the plugs on all electronic devices, TV included, so no one can watch anything. I have a 3 year-old who knows when we're on the computer we're not paying attention and does similiar things. Get a lock for the plugs and take the keys with you to work. No exceptions. I don't know what your husband does, but what you're talking about seems to be a fairly common complaint. The TV is an easy way to dump responsibility. Don't feel they'll miss anything, becasue they won't. They can watch TV and the computer under your supervision. We make our son earn his computer privledges: if he's bad, he loses the videos he likes to watch, if he's good, he may earn one or two extra.
Next, find a way to keep them out of the upstairs. Move rooms around, even if there's an inconvenience of toys in your living room. At least you know where they should hopefully be playing.
Also, lock up all the cleaning stuff or find some high cabinet your 5 year-old can't reach or climb to. Same thing, take the keys. If they need to clean, vinegar and baking soda work just fine with a little dish soap.
Also, set up a calendar of activities for them to do together. For example, your local library must have story times. Make a list of the parks they can go to. Invest in a few museam passes. Sometimes the only way I can convince my family to go with my son is to say we're wasting the money by not using the pass. I do either a weekly or monthly calendar and say we're going to do this on this particular day. Have backup plans for inclement weather. I have a list of places we can go in a pinch, and the mall isn't on that list. Find a group of stay at home dads for your husband. Make sure you ask daily what they did that day and ask for proof, even if it's just asking what they did. Have them bring the digital camera, your 5 year old can keep some type of journal, etc. Try to cater to your older one if at all possible. For example, if she likes birds, have her start keeping a birding journal. Make a calendar and ask her to write down what she did that day.
Finally, stockpile crayons, paper, etc. The libary should have tons of books on crafts and activities with kids, even basic cooking. M. Katzen is a great author for that. Put that on the calendar too for when they get home or later in the day. Make a meal plan and stick to it. I don;t know who cooks dinner, but your 5 year-old is capable of doing some basic measuring an mixing and it would be a sense of accomplishment on her part to help you do that.
Good luck!
A.