The ability to target cancer cells using an appropriate drug delivery system can significantly reduce the associated side effects from cancer therapies and can help in improving overall quality of life post cancer survival. Integrin $α5β1$ is expressed on several types of cancer cells, including colon cancer, and plays an important role in tumor growth and metastasis. Thus, the ability to target the integrin $α5β1$ using an appropriate drug delivery nano-vector can signficantly help in inhibiting tumor growth and reducing tumor metastasis. In this study we have designed functionalized stealth liposomes (liposomes covered with polyethylene glycol (PEG)) that specifically target the integrin $α5β1$. The PEG provides a steric barrier allowing the liposomes to circulate in the blood for longer duration and the functionalizing moiety, the PR_b peptide specifically recognizes and binds to integrin $α5β1$ expressing cells. PR_b is a novel peptide sequence, designed in our lab, that mimics the cell adhesion domain of fibronectin, and includes four building blocks, RGDSP (the primary recognition site for $α5β1$), PHSRN (the synergy site for $α5β1$), a (SG)5 linker, and a KSS spacer. In this study, we demonstrate that by optimizing the amount of PEG and PR_b on the liposomal interface we can engineer nano-vectors that bind to CT26.WT, HCT116, and RKO colon cancer cells in a specific manner and are internalized through $α5β1$-mediated endocytosis. Stealth liposomes functionalized with an RGD containing peptide bind to colon cancer cells and internalize, but they have much lesser efficiency than PR_b-targeted stealth liposomes, and more importantly they are not as specific since many integrins bind to RGD. PR_b-targeted stealth liposomes are as cytotoxic as free 5-Fluorouracil (5-FU) and exert the highest cytotoxicity on CT26.WT cells compared to RGD-targeted stealth liposomes and non-targeted stealth liposomes. In order to further increase the efficacy of the system we have designed peptide-functionalized stealth liposomes that are pH-sensitive and exhibit triggered release under mild acidic conditions present in endocytotic vesicles. The proposed targeted delivery system has the great potential to deliver a therapeutic load directly to colon cancer cells, in an efficient and specific manner.