First, congratulations for taking the time to exercise. It's an achievement by itself (considering many people want to, but don't end up doing it).
Second, If you really want to follow the StrongLifts 5X5 program, no, you cannot use dumbbells. You need to use a barbell and weights. Why?
For one, you cannot squat with dumbbells. The core of the program is progressively increasing your lifting weights by adding 2.5 lbs at every workout. You cannot do that with dumbbells.
For two, have you tried squatting (or bench pressing) with two 50-lbs dumbbells before? Have you tried the barbell equivalent? Which is harder? Yes, the dumbbells are much harder to do. So, it'll be impossible for you to follow the program with dumbbells.
Third, depending on your starting weight, you might not need a spotter initially. You're recommended to start with the empty barbell. Because you're increasing the weights in small increments, it's relatively hard to really injure yourself, unless you aren't paying attention to your body.
Fourth, as the weights you lift increase, the chance of injuring yourself increases as well. This is the time to worry about a spotter or a rack. You have a few options.
- Invest in a power rack. You can get something like this that doesn't take much space. Yes, it might seem a little expensive, but considering the potential health cost if you hurt yourself, this is a pittance. And it can be used for all the 5X5 exercises
- Join a gym that has a rack. Although the initial cost of this is lower than the first option, this cost adds up over time. The good news is that you'll usually have someone available to spot you, if you ask nicely :). Also, this option gives you access to a wider range of weights, so you don't have to purchase weight discs as you exhaust your current limit.
- Get any of your friends involved in the program. This way, they can spot you and you can spot them. Both of you reap the benefits.
BTW, if you decide to skip Strong Lifts, there are other compound exercise programs you can follow such as Starting Strength or Wendel's 5-3-1. However, they all require barbells and incremental weights.
Safety is very important and you should ensure you have the proper equipment and form for each exercise; otherwise, you can really injure yourself.
Whatever you decide to do, doing nothing is the worst injury you can inflict on yourself.
Go get stronger :).