You are talking about making a combined hash function from MD5 and SHA-1. Keep in mind that it is not trivial. For instance, if you just output both SHA-1 and MD5, you are actually only as strong as the weakest hash function (trivially for preimage, but also true for collisions, see [1]).

If you are interested in hash function combiners, have a look at Robust Multi-Property Combiners for Hash Functions [2], a recent paper on the topic. It aims at getting several properties at the same time (preimage resistance, collision resistance). For simpler schemes with a single property, just explore the bibliography at the end of the paper.

[1] https://cryptopals.com/sets/7/challenges/52

[2] https://eprint.iacr.org/2016/723

Using two algorithms together is basically just creating a new hash algorithm (with a longer hash), which could also have collisions.

If you know a technique for making SHA-1 collisions and a technique for making MD5 collisions, it's probably possible to combine the techniques and make a collision for SHA-1-MD5.